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VOL. I. 



Oxford University Press Warehouse 
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v. I 


The conception of Logical Science, which has been my guide 
in the present work, is that of an unprejudiced study of the forms 
of knowledge in their development, their inter-connection, and 
their comparative value as embodiments of truth. If an attempt 
founded on such a conception appears to err by over-ambitious- 
ness, I can only plead that an honest effort in the right direction 
does not depend for its value solely on its intrinsic success. It is at 
any rate a heavy wager laid by the author on his judgment of the 
true aim and future of his science, and may attain results as a 
suggestion which it misses as an achievement. 

In the present centrifugal state of logical research, no under- 
taking, perhaps, can be entirely valueless which aims at reintro- 
ducing some sort of unity into the enquiry. Such an aim is 
necessarily involved in the idea of a single connected science of 
logical processes and products. It has therefore been my object 
to maintain the central identity of judgment and reasoning 
throughout, and in no case to permit the variety of applications 
due to diversity of matter to interrupt the connection and sub- 
ordination demanded by unity of principle. Although in periods 
of transition logical science has been most effectually advanced by 
detached discussion, in separate chapters, ' books,' or volumes, of 
Inductive or experimental method, of equational reasoning, and of 
the Logic of Chance, yet it seems plain that a time must come 
when the various cases and species of inference shall fall into their 
respective places as organic members within the intellectual whole. 
But when this transformation is effected it is necessary that they 
should lose something of their interesting peculiarity and novelty ; 
and it is natural, from the difficulty of the task, that they should 

vi Preface. 

lose more of these qualities than is necessary. For this reason, as 
well as from incompetence in the field of exact science, I claim no 
discoveries in scientific method or in mathematical reasoning, but 
shall be content if my attempts to represent them have not many 
more errors than are either necessary or natural. 

There is in England a healthy objection to system-making, and 
a preference for free criticism, against which I should be sorry to 
offend. I think however that systematic form is essential to clear 
exposition and to really effective criticism, and I have not supposed 
that my work will be considered as a system in any other sense 
than that thus implied. In particular, I do not hope or even desire 
that the specific names which I have invented for some kinds of 
Judgment and argument should come into general use. I have 
endeavoured in every case to retain the accepted usage of the 
generic names, which are all that are recognised in ordinary logical 
discussion, and have only used strange titles for subdivisions which 
have no accepted place in existing logic, and which merely serve to 
insist upon certain views of logical evolution. 

It is almost superfluous to acknowledge here what I owe to other 
writers, as the Index bears copious testimony to the amount of my 
borrowings. In bringing together ' Inductive ' and ' Deductive ' 
Logic I have followed more particularly Sigwart and Jevons ; in 
the arrangement and analysis of Judgment-forms and forms of 
Inference I have gone to a great extent in the track of Lotze, and 
also of Hegel, to whom, so far as I know, the idea of this organic 
treatment of Logic is primarily due ; and in fundamental theory of 
judgment as in many details I owe even more, probably, than I have 
acknowledged, to Mr. Bradley, whose work, ' Principles of Logic,' 
appears to me no less valuable now than it did three years ago 1 . 
On one particular point, relating to the simplest process of equa- 
tion (colour-equation, for example), I am especially indebted to 
Mr. Spencer's Psychology. 

Every student will understand that my obligation to former 
writers is frequently as great when I diverge from them as when 

1 See the author's Knowledge and Reality, a Criticism of Mr. Bradley's 
14 Principles of Logic." ' Kegan Paul, Trench & Co. 1885. 

Preface. vii 

I assent to their opinion. As I have often been led to express 
disagreement with Lotze, portions of whose views certainly appear 
to me strange in so eminent a philosopher, I ought to say that but 
for his great work on Logic the larger part of what I have written 
would never have come into my head. I may also express my 
strong conviction that the reform of Logic in this country dates 
from the work of Stuart Mill, whose genius placed him, in spite of 
all philosophical short-comings, on the right side as against the 
degenerate representatives of Aristotle. A glance at the Index will 
suffice to show how constantly I have referred to his treatise. 

I may venture, finally, to discharge an obligation of older 
standing, and at the same time to emphasise the guiding idea of 
my work, by observing that the first germ of unprejudiced interest 
in the forms of knowledge was implanted in my mind, when wholly 
innocent of Hegel or Lotze, by some remarks made in a course of 
Logic lectures which I had the good fortune to hear about twenty 
years ago, the lecturer being Mr. Alfred Robinson, of New College, 
Oxford. A comparison, which he threw out, between the study 
and analysis of judgment-forms and the study and analysis of the 
forms of flowers or plants has never left me since, and I have never 
seemed to myself able to exhaust its suggestiveness. If I have at 
all reproduced for others the spectacle of continuity and unity in 
the intellectual life, combined with the most varied and precise 
adaptation of its fundamentally identical function to manifold con- 
ditions and purposes, which this comparison never fails to present 
to my own mind, I shall so far have -succeeded in the object of 
my work. 


London, April, 1888. 


VOL. I. 



1. Title of the work explained I 

2. Knowledge and its content 2 

i. Truth 2 

ii. Meaning 4 

3. What is the knowledge which we investigate ? 6 

4. The act of Naming 8 

5. What that act implies 13 

i. Logical significance 13 

ii. Meaning of ' implies ' 16 

iii. Objectification 18 

iv. A positive content . .19 

v. Meaning of Verb- and Case-endings 20 

vi. Naming and distinction 22 

vii. Naming and Comparison 26 

6. Concept and Judgment 30 

7. Logical meaning and the individual mind 41 

8. Intension and Extension 46 

i. Intension and Extension complementary and inseparable . . 46 

a. Their nature 46 

j8. Fictitious Ideas 48 

7. Nonsensical expressions 48 

8. Names of Attributes 48 

. Proper names . . . . " . . . . 50 

. Names with number attached 54 

ii. Alleged inverse ratio of Extension to Intension .... 58 

a. Mathematical phrase wrong 59 

)3. Greater Extension and Intension may go together, and 

lesser likewise 60 

7. Subsumption not the sole principle of reasoning . . 62 

iii. Truth of the inverse ratio . 63 

a. Alternative Classification . . . . . . .63 

j8. Higher individuals and abstractions 65 

7. Inverse ratio justified by natural classification ... 68 

x Table of Contents. 

Book I. The Judgment. 


Of Judgment and Judgment-forms in general. 


I. Nature of Judgment as such 72 

i. Symbolic Ideas 73 

ii. Reference to Reality 76 

iii. Judgment and Proposition 79 

a. The parts of the Judgment 80 

/3. Judgment in relation to Time . . . . .85 

1. Arriving at Judgment 85 

2. The complete Judgment 86 

II. Arrangement of Judgments 90 

i. Purpose of Scheme . 92 

ii. Explanations 93 

a. Use of the terms Categorical and Hypothetical ... 94 
, P. Divergent species of Judgment 96 

7. Use of the terms Analytic ' and ' Synthetic ' . . -97 

Quality and Comparison. 

Quality and Comparison . . . 104 

1. The Judgment of Quality 104 

i. Meaning of Quality 105 

ii. Judgment of Quality proper 105 

iii. Demonstrative Judgment 114 

2. The Judgment of Comparison 116 

i. Quantitative 1:7 

ii. In space and Time as such 120 

iii. So-called Qualitative 123 


Quantity and Proportion. 

The Judgment of Measurement 128 

1. Measurement and Individuality 128 

i. Simple measurement. Pure Quantity . . . .129 

ii. Complex, mediate or ideal measurement. Proportion . 131 
iii. Qualitative unity of Individual . ,. . . . .139 

iv. Change and Motion as revealing Individuality . . 140 
v. Abstraction and Necessity . . . . . .143 

vi. Absolute and Conditional affirmation . . . 144 
vii. Knowledge as union of absolute and relative . . .151 

Table of Contents. xi 

Measurement (continued) Abstract Quantity. 


2. One-sided forms of measurement 154 

i. Enumeration and Simple Counting 154 

Corollaries: a. Simple Counting . . . .156 

P. Discrete and Continuous . . .159 

ii. Judgments Affiliated to the Enumerative Judgment . .160 

a. Plural or Particular Judgment 160 

j8. Collective Judgment 162 

7. Enumerative Judgment reverting towards Generic, 

Exhaustive Judgment 168 

5. Judgment of Complex or Mediate Counting, Addition 

and Multiplication. The Equation ___ 1 ^^ . . 170 

6. Abstract Enumeration and the Infinite Series . .172 

Abstract and Infinite Time 178 

77. Abstract and Infinite Space 184 

a. Measurement of actual distances . . . .185 

b. Theoretical relations of spatial attributes . . 187 

(1) Individuality of figures in Space . . 187 

(2) Existence of figures in Space . . . 191 

(3) The quasi-generic Judgment . . . 195 
3. Infinite Space 197 

iii. Mechanical view of Universe and general relation of 

Equation to Judgment 200 


Singular and Universal Judgment. 

Singular Judgment 208 

i. Individual Judgment . .208 

a. with Proper Name 208 

/3. with Name and ideas 210 

ii. Corporate Judgment 212 

iii. Existential and Temporal element in the Singular Judgment . 214 

Universal Judgment 220 

i. Generic Judgment 222 

a. Quasi-collective Judgment 224 

P. True Generic Judgment 226 

a. Analogical Judgment 226 

b. Its existential meaning 237 

c. Individual (Generic) Judgment 242 

xii Table of Contents. 


Universal Judgment [continued). 


ii. Pure Hypothetical Judgment 249 

a. Its relation to previous forms 249 

/9. Its external form 250 

7. The assertion which it makes 252 

a. The idea of Ground . 253 

b. The idea of Cause 264 

(1) Cause as corresponding to Complete Ground . 264 

(2) Cause as an event ; i.e. distinguished from Ground 

Complete or Incomplete .... 266 

c . The element of supposition in universal Judgment . 2 78 

(1) Historical relations of simple and hypothetical 

judgment 283 

(2) The basis of hypothetical judgment . . . 287 

Negation, Opposition, and Conversion. 

1. Negation how related to Affirmation 293 

2. Bare Denial and the Infinite Judgment . . . . . . 297 

3. Significant Denial 300 

4. Opposition and Conversion 310 

i. The opposition of Judgments 311 

a. In the case of Singular Judgments 311 

)3. In the case of Particular Judgments 311 

7. In the case of Generic Judgments 313 

5. In the case of Hypothetical Judgments . . . . 315 

ii. Double negation 319 

iii. Conversion . 324 

a. Simple Conversion of Singular . . . . . . 325 

)3. Conversion by limitation 326 

7. Modal Conversion 329 

S. Simple Conversion of Universal Negative .... 330 

f. Contraposition 331 

5. Privation as warrant of Affirmation and of Exclusion . . . .332 

a. Privation and real possibility 333 

/3. Privation and impossibility 335 

Table of Contents. 


Disjunction and the Statement of Chances. 

The disjunctive judgment . 

i. Genesis of the disjunctive judgment 
ii. Imperfect disjunctions 
a. Not exclusive . 
/J. Disjunctions of Ignorance 
7. Disjunctions referred to point of Time 
Logical affiliation of true disjunction 
a. The Generic judgment 
0. The hypothetical judgment 
When are parts disjunctively related ? 
v. Is Disjunction reducible to Hypotheticals ? 

2. The statement of chances 

i. Limits of the problem in present work 
Affiliation of the abstract disjunction 
Essence of the statement of chances . 
iv. Applications of the statement as calculus 
a. Alternatives and Results . 
/3. Physical Alternatives 
7. Interesting Results .... 
v. What does statement of chances represent ? 

vi. Chance and series 

a. Fallacies relating to series 
/3. Causal inference from series 
7. Coincidence of observed and calculated series 
5. Series a reality for some purposes 
Probability of Judgments in the absence of Knowledge 










1. Kant's view of Modality fundamentally just 377 

2. The Problematic Judgment 380 

i. Nature of mere suggestion or question 380 

ii. Is the Problematic Judgment a form of the Apodeictic Judgment? 382 

a. The Particular Judgment the exception and the instance 383 

/3. The modal Particular negative and positive possibility . 385 

7. Essence of the Problematic Judgment .... 388 

3. The Assertory Judgment 389 

4. The Apodeictic Judgment ......... 391 

i. The hypothetical judgment 391 

ii. The disjunctive judgment 397 

xiv Table of Contents. 


Book II. Inference. 

The Nature of Inference. 


1. The Essence of Inference > . i 

2. Some Accidents of Inference 4 

i. Mental transition in Time 4 

ii. Discovery or novelty 8 

iii. Omission of relevant matter 9 

iv. Selection, and omission of irrelevant matter? . . . T3 

v. Three terms ? 13 

3. The lower limit of Inference 14 

i. The reproduction of Ideas 15 

ii. General necessity of Judgment t6 

iii. Specific necessity of Judgment 18 

iv. The true immediate Inferences 20 

a. Comparison 21 

/3. Abstraction 21 

7. Recognition 24 

5. Discrimination, etc 26 

. Inferential character of above processes . . . .26 

. Comparative Science . . . . . . 27 

4. Species of Inference which have been erroneously identified with its 

principle 29 

i. Inference from particulars to particulars 29 

ii. Subsumption 30 

iii. Calculation and equation 31 

a. Calculation proper 32 

/3. The logical calculus 33 

iv. Construction 36 

a. Physical 36 

0. Imaginative 38 

7. Intellectual, in geometry and mechanics . . . 39 

8. Intellectual, without limitation to geometry and mechanics 40 
Scheme of types of Inference . 42 


Enumerative Induction and Mathematical Reasoning. 

1. Enumerative Induction . . . . 43 

a. Syllogism in fig. 3 44 

/3. Divergent tendencies ....... 45 

7. The Individual Judgment in Induction (Lotze) . . 46 

Table of Contents. xv 


2. Mathematical Reasoning 48 

i. Number and Analogy Divergence 49 

a. Complete Enumeration as false Ideal. Syllogism and In- 
duction 49 

0. Enumeration as Arithmetical computation . . . 51 
7. Calculation compared with argument . . . -54 

ii. Applications of Calculation 56 

a. Substitutive Inference 57 

(/3. Apprehension of Connections in Space and Time) . . 59 

7. Calculation applied to Geometrical Reasoning. The Con- 

stitutive Equation 63 

8. Calculation applied to disparates. Proportion . . 68 

(1) Homogeneous Terms 68 

(2) ' a and a ' series 69 

. Proportion, Analogy, and the Hypothetical Judgment . 73 

. Consciousness and Conservation of energy ... 74 

iii. The mechanical aspect of Knowledge 77 


Analogy and Enumerative Induction. Examples 
Logical criticism of the Analogical argument 

i. Fig. 2. Undistributed middle, Import of this defect 

ii. Real value of Analogical argument . 

iii. No ratio of Identities to Differences 

iv. Concurrent Analogies. Negative confirmation 

v. Divergent tendencies in Analogy . 




Scientific Induction by Perceptive Analysis. 

1. Negative Inference 108 

i. Its nature and conditions 108 

ii. No conclusion from two negatives in 

iii. The negative instance 115 

2. Scientific Induction 117 

i. Induction and other Inference 118 

ii. Induction as Perceptive Analysis 122 

a. Symbolic expression of the problem 122 

#. Establishment of ordinary Hypothetical Judgment . .124 
7. Establishment of reciprocal Hypothetical Judgment . .128 

S. Conversion or Generalisation 13 

xvi Table of Contents. 

iii. Logical character of Perceptive Induction . . . .133 

a. Its essence as Inference 133 

P. Theoretical purpose of representation by symbols . .135 

7. Part played by number of instances 136 

(1) In Perceptive Analysis proper . . . .136 

(2) In assigning known effects to classes of unknown 

conditions 137 

iv. Observation and Experiment 143 

a. Natural Experiment 143 

P. Observation with accurate instruments . . . . 144 

7. Experiment expressed in logical symbols . . . . 145 

5. Experiment with the Siren analysed 149 


Scientific Induction by Hypothesis. Generalization. 

1. Hypothesis and Postulate 155 

i. -Hypothesis falls outside Postulate 155 

ii. But not if Hypothesis alleges Vera causa 158 

2. Phases of Hypothesis 159 

i. Rudimentary Hypothesis 159 

ii. Mediate Hypothesis 160 

a. Hypothetical nature of Induction t6o 

/3. Example of fusion between Hypothesis and data . .161 

3. Generalisation 168 

i. ' From many to all ' exploded 168 

ii. By mere determination 169 

iii. Material or Analogical Generalisation 170 

4. General view of Induction 175 

i. Difference from Jevons 175 

ii. Ultimate nature of Induction 176 


Concrete systematic Inference. 

1. Philosophical Subsumption 180 

i. Logical content of these Inferences . . . . . .186 

a. Real system 186 

j3. Apodeictic sequence 186 

ii. Their form, Syllogism in fig. 1 . . . . . .188 

2. Disjunctive reasoning 190 

3. The judgment of value 195 

i. Real Teleology . . . 195 

ii. Mediation 196 

Table of Contents, xvii 

I 9 7 

Recapitulation of the main characteristics of Inference 
i. No antecedent scheme of Inference . 
ii. Conditions of Inference .... 
iii. Relation of Syllogism to these conditions 

a. The traditional syllogism . 

jS. The syllogism as reasoned judgment 

The Relation of Knowledge to its Postulates. 

The formal postulates of Knowledge 205 

i. The Law of Identity 207 

ii. The Law of Contradiction 208 

iii. The Law of Excluded Middle 210 

iv. The Law of Sufficient Reason and Law of Causation . .212 

The material postulates of Knowledge 214 

i. The maintenance of life 216 

ii. The reality of human purposes 219 

The ultimate nature of Necessity 221 

A priori necessity and mediation 221 

a. Mediate nature of necessity forgotten in controversy . .222 
. Organised and unorganised experience, with ambiguity of 

test by Conception 224 

ii. Rehabilitation of formal distinctions in Logic . . . .228 

iii. Criticism of ' Aesthetic ' necessity 231 

a. Aesthetic necessity as a contradiction in terms . . .232 
j8. Aesthetic necessity as a mere case of logical necessity . 233 

VOL. I. 


1 If it is held a valuable achievement to have discovered sixty and odd species 
of parrot, a hundred and thirty-seven species of veronica, and so forth, it 
should surely be held a far more valuable achievement to discover the forms 
of reason ; is not a figure of the syllogism something infinitely higher than a 
species of parrot or of veronica ? ' Hegel, Wissenschaft der Logik, p. 139. 

1 We have seen that the members of the same class, independently of their 
habits of life, resemble each other in the general plan of their organisation. 
This resemblance is often expressed by the term " unity of type " ; or by saying 
that the several parts and organs in the different species of the class are homo- 
logous. The whole subject is included under the general term of morphology. 
This is one of the most interesting departments of natural history, and may 
almost be said to be its very soul.' Darwin, Origin of Species } p. 382. 

I. In giving to the present work the title of ' Morphology Title 
of Knowledge ' I intended to indicate as its purpose the ^* 
unprejudiced study of judgment and inference, throughout 
the varied forms in which their evolution may be traced 
and their relationships determined. Mere classification, 
therefore, or mere enumeration of the species of judgment 
or of inference, would not achieve the aim which I have set 
before myself, although I am wholly of Hegel's mind when 
he says that the species of syllogisms are at least as well 
worth discovering as those of parrots or of veronicas. The 
two quotations which stand at the head of this Introduction 
may together exhibit my conception of a logical system, 
if interpreted to mean that I would treat the forms of 
judgment and of inference as science treats the forms of 
animals or of plants, not in the spirit of enumerative classi- 
fication, but in the spirit of morphological analysis. In the 
Conception so determined, however, one further correction 
must be made. Morphology, as the science of external 
shape, involves, I understand, an antithesis to physiology as 
the science of vital function. This contrast belongs to the 
distinction of outer and inner, of persistent bodily form 
?* VOL. I. B 

2 Introduction. lintrod. 

and living productive process, which appears at first sight 
to prevail in the world of visible and tangible matter. 
Were we to transfer any such contrast to the scientific 
treatment of intelligence, we should obviously be forced to 
identify the morphology of knowledge with the science of 
language or of grammar, and reserve for the analysis of 
the vital thinking function some such appellation as that of 
Mental Physiology. I do not say that such an antithesis 
would be false, but it would fail to illustrate the point of 
view on which I am now desirous to insist. In the sys- 
| tematic activity of thought the contrast between bodily 
shape and vital process is non-existent. Even the evolu- 
tion of the animal organism might be considered as the 
development of a function which is a system of functions, 
and the science of life if thus regarded would unite, as it 
appears to me, what is valuable in morphology with the 
essence and spirit of physiology. Of the system of know- 
ledge, at any rate, this is the true account. The form of 
thought is a living function, and the phases and moments of 
this function are varieties and elements of the form. There- 
fore the 'Morphology of Knowledge' must be construed 
as not excluding the Physiology of Thought. The science 
of intellectual form includes the science of intellectual 
Knowledge 2- Knowledge involves the ideas (i) of Truth and (ii) of 
Content Meaning. i. How does the analysis of knowledge as 
Truth. a systematic function, or system of functions, explain 
that relation in which truth appears to consist, between 
the human intelligence on the one hand and fact or 
reality on the other? At first sight, even the genetic 
analysis of a systematic development which we propose 
to undertake, though a more genuine explanation of 
that development than any mere summary of types, 
is powerless to grasp the relation between the system 
so developed, and an object-matter that lies outside 
it. To this difficulty there is only one reply. If the 
object-matter of reality lay genuinely outside the system of 


INTROD.] Tl'lltk. 3 

thought, not only our analysis, but thought itself, would be 
unable to lay hold of reality. For logic, at all events, it is . 
a postulate that ' the truth is the whole.' The forms of < 
thought have the relation which is their truth in their 
power to constitute a totality ; which power, as referred to 
the individual mind, is its power to understand a totality. 
The work of intellectually constituting that totality which 
we call the real world is the work of knowledge. The 
work of analysing the process of this constitution or deter- 
mination is the work of logic, which might be described as 
the self-consciousness of knowledge, or the reflection of 
knowledge upon itself. Logicjhasj io cr ite rion of tru th nor * 
test ^ of reaso ning. Truth is individual, and no general 
principle, no abstract reflection, can be adequate to the 
content of what is individual. It is indeed impossible to 
study the growth of knowledge without lighting upon 
confusions of thought that evoke a warning word. But 
even a confusion of thought may have a material signifi- 
cance, and therefore contain a material truth, which escapes 
the logical critic who perforce ignores its individual content. 
The relation of logic to truth consists in examining the 
characteristics by which the various phases of the one in- 
tellectual function are fitted for their place in the intellec- 
tual totality which constitutes knowledge. The truth, the \ 
fact, the reality, may be considered, in relation to the 
human intelligence, as the content of a single persistent and 
all-embracing judgment, by which every individual intelli- 
gence affirms the ideas that form its knowledge to be true 
of the world which is brought home to it as real by sense- 

The real world for every individual is thus emphatically ( 
his world ; an extension and determination of his present 
perception, which perception is to him not indeed reality . 
as such, but his point of contact with reality as such. 
Thus in the enquiry which will have to be undertaken as to 
the logical subject of the judgment, we shall find that 
the subject, however it may shift, contract, and expand, 

B % 


4 Introduction. [introd. 

is always in the last resort some greater or smaller 
element of this determinate reality, which the individual 
has constructed by identifying significant ideas with that 
world of which he has assurance through his own per- 
ceptive experience. In analysing common judgment it is 
ultimately one to say that / judge, and that the real world 
for me, my real world, extends itself, or maintains its 
organised extension. This is the ultimate connexion by 
which the distinction of subject and predication is involved 
in the act of affirmation or enunciation which is the 
differentia of judgment. 
Meaning. ii. To speak of consciousness as a single persistent judg- 
ment is at first sight a paradox, in view of the distinction 
between an idea and the affirmation of an idea. It is 
not easy to deny that there is a world of ideas or of 
meanings, which simply consists in that identical reference 
of symbols by which mutual understanding between 
rational beings is made possible. A mere suggestion, a mere 
question, a mere negation, seem all of them to imply that we 
sometimes entertain ideas without affirming them of reality, 
and therefore without affirming their reference to be a 
reference to something real or their meaning to be fact. 
We may be puzzled indeed to say what an idea can mean, 
or to what it can refer, if it does not mean or refer to some- 
thing real to some element in the fabric continuously 
sustained by the judgment which is our consciousness. On 
the other hand, it would be shirking a difficulty to neglect 
the consideration that an idea, while denied of reality, may 
nevertheless, or even must, possess an identical and so in- 
telligible reference a symbolic value for the rational 
beings who deny it. A reference, it may be argued, must 
be a reference to something. But it seems as if in this 
case the something were the fact of reference itself, the 
rational convention between intelligent beings, or rather the 
world which has existence, whether for one rational being 
or for many, merely as contained in and sustained by such 
intellectual reference. 

Introd.] Meaning. 5 

I only adduce these considerations in order to explain 
that transitional conception of an objective world or world 
of meanings, distinct from the real world or world of facts, 
with which it is impossible wholly to dispense in an account 
of thought starting from the individual subject. The para- 
dox is that the real world or world of fact thus seems for 
us to fall within and be included in the objective world or 
world of meanings, as if all that is fact were meaning, but 
not every meaning were fact. This results in the contra- 
diction that something is objective, which is not real. 

We do not meet this paradox adequately by reminding 
ourselves that e.g. a negation or a question is a fact in 
some one's mind, and therefore as a psychical occurrence 
is a real event, and in that sense falls within reality. In 
considering an idea as a psychical occurrence we abstract 
from its meaning, which apparently consists in some identity 
or persistent unity that extends beyond the isolated occur- 
rence of the idea in time. 

The solution of the difficulty appears however to be 
suggested by the distinction which we have just taken. As 
the psychical occurrence and objective reference are dis- 
tinguishable by abstraction only, so objective reference 
and reference to reality (affirmation) are distinguishable by 
abstraction only. The world of objective reference and the 
world of reality are the same world, regarded in the former 
case as composed of isolated though determined contents, and 
in the latter case as composed of contents determined by 
systematic combination in a single coherent structure. The 
former point of view is an abstraction that goes near to be a 
fiction, for isolated contents qua isolated are not determined. 
But it is possible and usual to consider ideas, by help of 
abstraction, in respect of those relations which especially de- 
termine them, as detached islands or spheres of knowledge, 
without actually referring them in a thoroughly determinate 
judgment to a place in the one individual system which for 
each of us is the reality. Ideas thus isolated are what we 'en- 
tertain' as significant or symbolic ideas which have meaning 

6 Introduction, [Introd. 

or objective reference, and yet are not affirmed of Reality. 
Objective reference is the substance of the convention by 
which rational beings communicate with each other and 
with themselves, and which, though a consequence of the 
unity of Reality, can be regarded without being directly 
identified with that unity. To show that every idea which 
is entertained, as for example suggested or supposed, must 
be taken to be tdtimately affirmed of reality, is the task of 
those portions of logic which deal with question, suggestion, 
supposition, and denial. Thus in the discussion of mere or 
bare denial we shall be forced to the conclusion that where, 
in an attempted judgment of denial, no positive basis nor 
positive consequence of the denial is to be discovered, 
where, that is, the idea which is verbally denied forms no 
element in any affirmation of any kind about Reality, there 
no judgment can really take place, nor can the idea in 
question be enunciated as an intelligible idea. The mean- 
ing which an idea seems to retain when named in a spurious 
judgment or unintelligible proposition of this kind depends 
on its initiation of other acts of thought than the denial in 
which, ex hypothesi, we were to look for its unaffirmed 
signification. Our treatment of supposition will lead us to 
the same result. All significant, i.e. all logical, ideas are 
ultimately elements in a single judgment, the judgment 
which sustains the ideal structure of the real world. 

Thus the world of truth and the world of meaning are 
not really distinct, and the process which logic investigates 
is the single process and individual self-determination of 
the whole which is the truth or reality. 
What 3- It is natural to ask, ' Where and what is this self- 

knowledge determination? Where does it begin? Where does it 

are we in- 

^estigat- end? Is it in the individual mind or in the history of the 
race, or in an arbitrary combination of the two ? ' 

I cannot attach much importance to this question, which 
might be asked with equal justice, as it appears to me, of 
every science. A science deals with its object-matter 
wherever it finds it. The self-determination of the knowing 

introd.] What knowledge are we studying ? 7 

intelligence as the real world takes place wherever there is 
knowledge and in as far as there is knowledge. If the 
question is whether the process as described is necessarily 
involved in knowledge or is a mere fact like any isolated 
fact, there can be no answer except that the question is 
either superfluous or meaningless. Of any particular logical 
theory, such as that contained in the present work, it is 
superfluous to ask whether it is in all respects necessary 
and absolute. Of course it will contain many erroneous 
and many accidental elements. But to ask whether a true 
account of the logical process would be necessary and 
essential, or would contain mere fact or accident, is simply 
to ask whether a true account may not perhaps be false. 
All truth is necessary in as far as it is rationally known. 
And if a scientific analysis were to lead to no truth at all, 
it would simply lead to nothing. Whether in any particular 
instance such a nothing may have resulted is a matter for 
consideration on the merits of the individual case. But 
in general I must protest that there is no more reason in 
asking what evolution of thought we are studying, than in 
asking what laws of motion are studied by mechanical 
science. The laws of motion express the characteristics of 
moving bodies qua moving ; and the laws of knowledge 
express the characteristics of knowing subjects qua knowing. 
It is no more necessary to specify in what particular cases 
you find knowledge, than to specify in what particular 
cases you find motion. If knowledge has a nature that 
can be studied and if not, there is no logic it can only 
exist where that nature is realised ; and however the pro- 
gress of the race may have prepared the intellectual in- 
heritance which is devolved upon successive individuals, 
those individuals can only make it their own by fulfilling 
the conditions which constitute its nature. I do not deny 
that the type and content of knowledge must change with 
the advance of evolution ; I only affirm that any such 
change depends on the modes and degrees in which the 
general conditions of knowledge are fulfilled in successive 

8 Introduction, [introd. 

generations, and not in any difference between knowledge 
in its essential nature, knowledge as developed in the race, 
and knowledge as a process within the individual intelli- 
The act of 4. To give a name is for civilised thought the first 
Naming. ste p j n k now l ec ige. It at once depends upon, and in a 
sense creates, a recognisable arrangement of things, quali- 
ties, and relations. Wherever new ground has to be 
appropriated, whether actually or in metaphor, the first 
necessity is to find recognisable points, by which, being 
named, we can observe and communicate our where- 

The value of this first step is only to be estimated by 
experience, now necessarily exceptional, of the attempt to 
attain knowledge without it. We do not experience this 
simply by going where a language is spoken that we do 
not understand. No doubt, in the long run, lack of com- 
munication with our fellows would affect our reasoning 
power ; but we are now looking for an instance in which 
we ourselves, within our minds, have no names to aid us in 
distinguishing and recognising things. We find such an 
instance in our attempts to deal with any new region of 
knowledge of which we have not mastered the rudiments 
and in which we have neither books nor teachers to guide 
us. This is merely individual ignorance; but the great 
pioneers of knowledge must be in the same predicament 
when, going beyond established distinctions and taking 
note of new phenomena, they lay the foundations of a fresh 
structure of science. Great discoverers are able to add 
fresh names to language ; ordinary men content themselves 
with learning the meaning of those in common use. The 
\ limitations of popular nomenclature form the limitations of 
I popular observation. When we are brought face to face 
with a scientific classification and the terminology it in- 
volves, we are astounded at the blindness in which we had 
contentedly been living. Every yellow ranunculus we call 
a buttercup, every myosotis a forget-me-not, every large 

introd.] Naming. 9 

white umbellifer a hemlock ; not merely as an epithet, but 
because we really see no difference. So in the history of 
architecture or of fine art, popular knowledge is confined 
for the most part to the application of two or three terms 
which have gained currency. Few people are able to 
observe without the help of names. 

It is true that there is something ludicrous in the 
tendency of common minds to cling to a name ; in the 
insistance of an inexperienced art-critic on superficial 
characteristics which happen to be nameable, when he 
ought to be looking into the special significance of a work 
of art ; in M. Jourdain's delight at the discovery that he 
conversed in prose, or in the sudden zeal of Strepsiades 
for the correct employment of the masculine and feminine 
terminations. Nevertheless, the current censure of verbal 
knowledge is itself largely founded on ignorance, and 
actually on the same ignorance which creates the risk and 
opprobrium of mere verbal knowledge. In the annals of 
philosophy there is nothing more tragi-comic than Mill's 
condescending excuse for Plato's discussions about related 
existence discussions which laid the permanent foundations 
of scientific logic; the modern logician showing his superiority 
to verbal quibbles by an attempt to dissociate existence from 
attribution based simply and solely on the fact that existence 
is sometimes expressed by a peculiar kind of attribution. 
The condemnation of a knowledge which rests in mere words 
too often means that the word and no more has reached the 
understanding of the critic. It is probable that we think 
too little rather than too much of Naming as a first step in 
knowledge. To give names which endure is with few 
exceptions the prerogative of genius. The number of 
terms which we inherit from Plato and Aristotle is among 
the most striking proofs of the immense advance which 
they won for the human intellect. These two great minds 
mapped out the world of knowledge in its essential features 
much as we have it before us now, and gave to its main 
divisions the names which they still retain. Or, again, 

io Introduction. [introd. 

what a gigantic advance was made by the work of Linnaeus, 
though it now serves as the stock example of an ' artificial ' 
classification ! It was the indispensable starting-point for 
the more profound and rational researches of modern times, 
and thus if not one of the most arduous, at least one of the 
most valuable, of scientific achievements. 

I spoke of Naming as the first step in knowledge for 
civilised thought. Plato recognised the operation much as 
we recognise it. And yet there must have been a time 
when it was not easy thus to isolate a single word from the 
sentence. Indeed, even now, the single word is not really 
isolated. Except in the instances in a logical text-book, 
the utterance of a single word always implies a sentence, 
and usually a judgment. We now print the title of a book 
or the description of a species of flower, contrary to older 
custom, without a verb ; but none the less they are read off 
into propositions or judgments. The artificial nature of the 
supposed concept which is thought to correspond to a 
name and to be generically other than a judgment is 
curiously illustrated by the fact that Linnaeus was the first 
to omit the verb in the descriptions of flowers. Such des- 
criptions, though in appearance reduced to logical names, 
are of course understood as sets of judgments. No doubt 
however all these habits, including the use of dictionaries, fa- 
miliarise us at least with the. appearance of the significant noun 
in complete isolation from the sentence, and lead us to ima- 
gine that in such isolation it is still a fair representative of 
some individual object or quality (also isolable) in a way in 
which the complete sentence is not. But I must repeat that 
under no circumstances does a man in his senses make use 
of an isolated noun, except to indicate an assertion, wish, 
or command. A dependent sentence, as its name shows, 
cannot stand alone ; and a name is for grammar in this 
respect like some form of dependent sentence. If a man 
were to say ' the sun,' the difference between this and a 
given proposition like 'the sun is low,' is not that in the 
first case we have a mere name and in the second a propo- 

introd.] Isolation of the Name. 1 1 

sition, but that in the second case we have a given pro- 
position, while in the first we are set to make propositions 
at random. The same is true of any logical noun, i. e. 
descriptive or appositional sentence and a noun may, we 
shall see, be equivalent even to a conditional sentence 
such that it can stand as subject or predicate in a propo- 
sition. No such sentence is ever used independently; for 
all thought, if not optative or imperative 1 , is categorical. 

Thus it would seem that the isolation of the significant 
name from its context, which is even now more apparent 
than real, must in very early stages of language have been 
a wholly unfamiliar process. The history even of proper 
names shows a tendency to illustrate this ; though proper 
names for human beings would be, one would suppose, 
among the earliest productions of language. As we go 
back, we find the ' proper ' name less purely distinctive, less 
1 proper,' and more significant or predicative. The animal 
names borne by some savages must be significant, though 
how or of what may be doubtful. The Roman Agnomen 
and the Athenian Deme name were directly significant, 
as of course are many modern surnames in their recent 
origin. The addition of a name of father (also husband or 
master) in the possessive case was not originally a mere 
appellation , it was an assertion of ownership 2 . It is well 
known that among the Romans the gentile name (nomen) 
was the name par excellence, as indeed for most purposes the 
surname is now. It is less well known that the 'fore-name,* 
which, if any, was individual, was not at all freely chosen to 
serve as a distinctive sign ; it was characteristic of family, 
and the choice was exceedingly restricted. Among all the 
Roman patricians only about thirty ' fore-names ' were in 
use, and the ' fore-name ' of women was constantly omitted 

1 Whether optative and imperative forms can or should be analysed into 
categorical propositions is a psychological rather than a logical question. 

2 Mommsen, Romische Forschungen, vol. ii. p. 5. He shows good ground 
for supposing that the original form was ' Marcus Marci,' used equally of wife, 
slave or son, and that Marcus Marci filius (no corresponding form was adopted 
in Greek) was a later modification. 

1 2 Introduction, [introd v 

in Cicero's time. It would be interesting to find parallels 
for some of these features in modern usage ; a small number 
of Christian names no doubt serves to name by far the 
greater number of individuals in one country, and the selec- 
tion of Christian names is to a certain extent characteristic 
of families or of family. But on the whole it is now admitted 
that the chief purpose of a proper name is to be a name, i. e. 
a constant sign, and even the surname, although significant 
in many respects, is not really to be relied on as an indica- 
tion of family. The law lets a man bear what name he 
pleases and change it as he pleases, so long as he makes his 
desire sufficiently well known ; in other words, the law accepts 
no purpose in the name beyond that of mere recognition. 

And in the case of the common or significant name the 
same thing is more evident. Even so highly modernised a 
language as classical Greek has no unambiguous expression 
for ' a word,' though ' noun ' and ' predicate ' or 'verb ' were 
familiar terms to Plato and Aristotle. The latter has to 
describe a ' word ' by the periphrasis, ' the least portion of 
discourse which is significant when taken by itself.' The 
Greeks did not separate their words in writing ; and in their 
inscriptions a terminal consonant is affected by the following 
initial consonant, as it would have been in a compound 
word. I do not think it is fanciful to refer to these facts in 
illustration of the closer cohesion of sentences in ancient 
than in modern speech. The solvent of the sentence is 
obviously writing. You cannot take to pieces the spoken 
sentence as you can that which lies written before you. If 
you ask an uneducated man about some one point in what 
he told you, he will say it all over again. But this 
enquiry hardly belongs to logic, though it helps to rouse us 
out of the analytic abstractions in which we are now at 
home. I only wished to guard myself against asserting 
that the conscious selection of an individual object and the 
appropriation to it of an element of language common to 
all sentences in which that object is referred to that this 
act of Naming comes first in history as it does in modern 

introd.] Logical Significance. 1 3 

science. It appears to me that the descriptive sentence 
must have furnished the material for a subsequent appro- 
priation of names ; and that the appropriation of names by 
habitual description must have .been quite a different pro- 
cess from methodically searching for new ' points d'appui ' 
and fixing their appellations at one blow. 

5. The act of Naming implies in the first place ' Logical What the 
Significance.' i. A name then is a sign which rouses the mind Naming 
to a set of activities having an identical element. In the implies. 
purely artificial case, when a name is spoken in my hearing gf f^. 1 
without any context expressed or implied, such activities cance. 
may probably take the shape of interrogation or suggestion ; 
i.e. as is commonly supposed (but see sect. 2, above), a 
review of matters which we might employ in judgments, 
but do not yet know how to, being unable to attach any of 
them to our real world. The meaning of the name consists 
in its power of suggesting and controlling these activities, 
these judgments completed or inchoate. If, to return to the 
example suggested above, I hear some one say ' The sun,' 
my first idea is that the speaker is thinking aloud, and 
that I have caught the fragment of a sentence which he has 
completed in his mind. But with a view to logical theory 
we may neglect the speaker's intention (though no theory 
should forget that it has neglected this feature of the case), 
and simply consider what the word does for the hearer. 
It makes him think of something, and in this case of what 
is called par excellence a thing : had the word been ' red,' it 
would have suggested a quality ; had it been ' parallel/ a 
relation. We have not to do just now with the difference 
between these three kinds of signification, but only with 
what signification is as such. In thinking of something 
without more guidance than a significant name, we find our- 
selves involuntarily thinking not merely of it, but about it. 
And this is inevitable. That which the name signifies is, 
for us at all events, an identical character exhibited by 
different contexts, or different contexts united by a common 
character. Any one who has been told, by an old-fashioned 

1 4 Introduction. [introd. 

mesmerist, to ' think of nothing but ' a copper and zinc 
disk which is put in his hand, and which he is expected to 
contemplate for some minutes, must have found (supposing 
that he attempted to do what he was told) that his thoughts 
traversed in a series of judgments the various ways in which 
the thing affected his perceptions, or reacted in the com- 
parisons that suggested themselves 1 . These judgments, if 
expressed in language as propositions, would all contain 
the same name, that of the thing which they described. 
But although connected with different standards of com- 
parison in the different judgments, the thing spoken of 
in them all is not different things, but the same thing. If 
you persevere and try to elicit the root and basis of its 
identity, you may indeed fix more or less arbitrarily upon 
certain ' essential ' attributes, but these attributes represent 
the thing in different contexts, and are also themselves, as 
Mill has explained 2 , elements of identity between different 
contexts. You may judge the thing to be round, hard, 
heavy, flat, cold, and to be on the palm of your hand, and 
you may define circular form, hardness, weight, etc. as you 
please ; but you will not express either thing or attribute 
as other than an element of identity which is exhibited and 
takes shape in different aspects or relations. Mr. Bradley 3 
has pointed out that extension in space or duration in time 
are sufficient to invest that which has them with the 
character of an identity into which differences enter. 
This an identical element which enters into and is entered 

1 I suspect that the particular mesmerist to whom I refer was influenced by 
the fallacy which has been combated in the text, and imagined that to think 
continuously of an individual thing involved an immobility of thought, as though 
the thing were for thought like an image in space fixed and isolated. In at- 
tempting to attain such an immobility (which attempt, on this hypothesis, the 
operator intended to be made) the patient would simply arrest the operation of 
his intelligence, and would thus approach to that withdrawal of attention from 
all specific stimuli which is perhaps a condition of the mesmeric sleep. How 
far this principle is connected with that of Braid's and similar experiments, 
I am not expert enough to say. Cf. Lotze, Metaphysik, sect. 304. 

2 See Mill's Logic, i. 201 (sixth edition). 

3 See Bradley's Principles of Logic, p. 44. 

introd.] Rational Convention, 1 5 

into by differences is what we might call the logical signi- 
ficance, the significance which must be postulated in all 
cases, of a name as such. 

The process of Naming, as known to our reflective 
thought, is to adopt an individual element of language 
as the instrument of intellectual reference to an individual 
identity in the knowable world. The conscious adoption 
or appropriation of the linguistic sign is the same thing 
in principle, whether the sign is employed solely within 
my own consciousness, or is applied to communication 
with other intellectual beings. The ' convention ' l or 
agreement which has been said to give language its 
meaning, would be the same thing between other persons 
and me that the employment of significant signs is be- 
tween me, so to speak, and myself. It is as wonderful, 
and as much a proof of ' convention,' i. e. of the power to 
agree, that ' goodness ' should mean the same to me yester- 
day and to-day, as that in this sentence it should mean the 
same to me and to my reader. It may be said, and here we 
anticipate a difficulty which must be treated later in this 
chapter, ' But goodness does not mean quite the same to 
you and to your reader, or to you at different times.' Then 
I will change the phrase and substitute ' refer to.' It will 
be seen at once that if ' goodness ' in my mouth and in 
yours does not refer to the same characteristic, it is not 
intended to mean the same, and its meanings however 
different cannot be conflicting. In that case the two charac- 
teristics referred to are ' homonymous/ and the same word 
goodness is used for them only by accident 2 , as glass is 
for a telescope and a tumbler. The point and purpose 
of a name is, always to refer to the same ; it is on this 
reference that the whole possibility of mutual intelligence 
depends. The connection between isolated reference, or 

1 A name is speech which has meaning according to convention {tcara 
cvv9t)KT)v). Arist. Ilepi 'Ep/xr]vdas, sect. 2. 

2 By accident as regards present use ; there may be a common history, but 
this is rather a source of deception than of clearness. 

1 6 Introduction. [introd. 

meaning, and reference to a system, or affirmation, has been 
explained above (sect 2). 

Identical reference or rational convention is thus the 
root and essence of the system of signs which we call lan- 
guage 1 . The act of Naming, i.e. of establishing such 
a reference, and of appropriating a sign to it, has been 
elaborately analysed into a number of processes or aspects. 
In my opinion such an analysis should be regarded mainly 
as a mere analysis as a distinction of aspects and not as a 
history of acts. Historical conclusions may flow from it ; 
but the analysis is the first thing. We are here met by a 
difficulty which besets all the higher sciences, and which I 
shall endeavour in the first instance to grapple with in its 
general form. 
Meaning of ii. The distinction of stages in a continuous growth has 
'implies. a i wavs a degree of artificiality. It is hard to say precisely 
when an embryo becomes a chicken, or a boy a man. It is 
impossible to say at what point feeling appears in the 
organic world, or when a child acquires a will, or a primitive 
tribe the instinct of religion or of fine art. Characteristics 
which attract general notice only when full-grown, are 
traceable far back when we come to look for them ; and 
further, they are frequently implied by the nature of an 
individual long before any scrutiny can detect them. It is 
a cheap and false accuracy to express such a growth in 
successive stages according to the definite emergence of 
obvious features, without scrutinising the continuous identity 
which is present from beginning to end. But it is a fatal 
carelessness, on the other hand, to treat rudimentary attri- 
butes as ipso facto equivalent to their mature form, or as 

1 I can see no ground for restricting the logical conception of language to 
written or spoken words. We must not argue from the possibility of educating 
the deaf and dumb (cp. Lotze, Logik, sect. 6) that 'the logical operation in the 
mind is independent of the possibility of linguistic expression.' It is unfortunate 
that the German ' Sprache ' and ' sprachlich ' make this inference appear a 
truism, while if we ask whether the deaf and dumb can in thinking dispense 
with fixed signs wholly or in part, the question, though still of interest, 
assumes a very different complexion. 

introd.] Continuity of growth. 1 7 

necessarily identical therewith in the features of chief con- 
cern. The labour of genuine science is to disentangle the 
true continuity of processes, limiting it only by modifications 
which are certainly traced or inevitably implied ; never 
assuming the existence of a highly developed attribute or 
function where it is not seen in operation, or shown to be 
implied to the exclusion of all conceivable alternatives. In 
fact, if ' conceivable ' means ' conceived up to a certain stage 
of knowledge,' the last clause is not stringent enough; a 
suspension of judgment is often preferable to a conclusion 
from disjunction which violates general analogy. Many 
complete-looking disjunctions are imperfect ; and unless 
supported on a thoroughgoing principle, a disjunction is 
worth nothing at all. 

It is hard to escape both the complementary blunders 
which I have indicated, and the object of this digression is to 
point out that though we may not escape them altogether, 
their sting is removed if we are not too ready with our dis- 
junctions, but discuss to the best of our power the principles 
which underlie functions and attributes, and the consequent 
limits and laws of their modifications. Have such and such 
savages the instinct of fine art ? Probably Yes or No would 
be no answer. We should find that they had some 
elements or germ of such a tendency, perhaps the love of 
imitation, or earlier still, the instinct of construction. 
Then we should have to estimate the value of this and its 
connection with aesthetic capacity; and the correctness of 
our whole reading of the facts would probably depend on 
the Tightness of this estimate. The act of naming presents 
such a problem. Does Naming, for instance, imply the 
processes of Comparison and Distinction ? Does it imply 
a Judgment, such as the Judgment of Perception ? If we 
look at the activity of highly reflective thought, we must 
unhesitatingly answer both questions in the affirmative. 
It is a serious matter to introduce a new word into lan- 
guage, or to christen a new phenomenon or a new species. 
All that science can do to verify and determine is being 

VOL. I. C 

1 8 Introduction. [introd. 

done when, and is largely done before, such an event 
occurs. Or if we go to the extension of the individual's 
knowledge, which is to him a creation of new appellations, 
the same holds good for kindred reasons. The individual 
profits by the work which language presupposes, and all 
sorts of apparatus is at hand by which he can put himself 
through the processes, in learning a name, which the dis- 
coverer went through before him in conferring it. This is 
the one extreme of the growth we have to watch ; the 
extreme at which the function we are discussing has 
become an instrument of conscious science. 
Objectifica- iii. In speaking of the opposite and lower extreme, we 
have to depend on analysis and implication. Let us think 
of the feature of reference , which we found to lie at the root 
of intelligent speech. A name always refers to something. 
(I must repeat that the idiomatic ' something ' is not to be 
taken as meaning an individual ' thing' in space.) I avoid 
saying that it refers to an idea in the mind, because, unless 
the name explicitly proclaims itself the name of an idea, it 
does not refer to an idea in the mind as such *. When I use 
the word ' red ' I do not refer to or mean my idea of red 
considered as my idea, though I do mean red as I under- 
stand it by help of my idea. When I use the word, I mean 
a colour, a quality of surface, or at least of light, which I 
represent to myself by help of one or more reds which I 
have seen, but which I think of as not dependent either for 
being or for quality on my happening to know it. The fact 
that my perception of red may be abnormal does not affect 
this reference. As I pointed out above, if it were not for 
the identical reference there could be no conflict, no question 
of normal or abnormal. This, then, if no more, is involved 
in naming. That which is named is recognised as having 
a significance beyond the infinitesimal moment of the 
present, and beyond the knowledge of the individual. It 
enters into the ' convention ' which he who uses language 
maintains with himself and with others. It is, in short, 

1 See below, ch. i. sect. i. 

introd.] A positive content. 19 

characterised as an object of knowledge 1 . Under this 
aspect the act of Naming has been well called the act of 

Let us further consider what is implied in the act of 
Naming considered as an act of Objectification. 

iv. In the first place, then, the matter which is invested with A positive 
the attribute of being such as to be known which is thus con en ' 
1 objectified ' must be something positive, something, so to 
speak, of affirmative nature 2 . It must be presentable to 
consciousness by help of some actual modification of con- 
sciousness. I mean that it cannot consist simply and solely 
in the distinction between itself and something else. It is 
one question how we come to perceive a certain content 
contrast and distinction may be essential to perception 
another what it has in it when brought into perception. It 
may be the question is chiefly psychological that if red 
had been the only colour we should never have been aware 
of it as red. But now, being aware of it, we find in it a 
positive quality or character which is not exhausted by the 
distinction between it and all other colours. This is the 
primary condition of the act of naming. That which is to v 

be referred to by a name, which is thus erected into an 
object for intelligence, must be at least a positive content, 
something with a nature and character. It is not safe to 
clinch the matter by saying ' definite nature,' ' determinate 
character ; ' for though scientific naming involves all this, 
yet it would be overbold, and would beg a question which 
we shall soon arrive at, to presuppose all this for every act 
of naming. ' Definite ' and ' Determinate ' introduce nega- 
tion into knowledge, and so are not words to be used lightly. 
We must if possible keep to one thing at a time, and what 
we are sure of at this point is this, that the identity in differ- 
ence which is referred to by a name is something positive ; 
not necessarily a 'quality' in the technical sense of an 
immediate unrelated matter of perception, but necessarily 
a something. 

1 Cp. Lotze, Logik, sect. 3. 2 Cp. Lotze, Logik, sects. 10, II, 

C 2 

20 Introduction. [Introd. 

It is obvious that for the general purposes of logic such 
meaning is not confined to substantive and adjective nouns 
or names. A positive content is also referred to by the 
material or uninflected element in verbs, if we may for 
logical purposes distinguish this from the formal or inflected 
portion, which indicates the connection and function of the 
verb as such. When I say ' it flows,' of course in the 
element ' flow' I use a significant sign which refers to a 
positive content. Very probably as we go back into 
primitive speech the distinction between this and the gram- 
matical Name would disappear. Aristotle certainly treats 
1 is white ' as a verb \ 
Meaning of v. Here we cannot escape raising a further question, 
case-end- Granting that pronouns used independently rank as nouns, 
ings. still. there remain inflected elements of verbs, the case- 

endings of nouns, adverbs, prepositions and conjunctions. 
Does not each of these indicate an identity in differ- 
ence, a positive feature in the world of meanings? Why 
are not they too to be treated as names ? There is no 
doubt that the words in question are fixed signs which refer 
to positive features of the world ; nor that their contents are 
such as can have names given them which can be employed 
in propositions as substantives or adjectives. Presence in 
time or space, Intention, Direction, Proximity, Property, 
Attribution, Reference, and the corresponding adjectives, 
these are all intelligible names and designate familiar 
matters. Yet they are but another shape of such linguistic 
elements as Here,' ' Now,' ' For/ ' To,' ' At,' ' Of,' ' About,' 
the s in ' flow.*-/ 

It would be easy to answer that these elements are signs 

1 He distinctly treats the prjfia as capable of indicating time. So his idea of 
it did not quite cover our Predicate, which he would call to KaTrjyopovfievov, 
though on the other hand we do not recognise ' is white ' as a verb. It is 
remarkable that he should have insisted on the indication of time in face of the 
fact (constantly borne out by his own instances) that the verb ' is ' could be 
omitted in Greek, and predication conveyed by position only. It seems therefore 
that to say the verb was understood would have been no empty phrase to him, 
but would have expressed the fact as he regarded it. 

introd.] The formative elements. 2 1 

whose content consists in the actual operations of thought ; 
that therefore they are not at first names, because we are 
operating directly and not reflecting on the operations ; but 
that they become names at the stage of reflection in which 
we become aware of the part played by our intelligence in 
connecting and comparing the data of sense-perception. 

But this would not be true. There are names for intel- 
lectual acts, such as Comparison, Measurement, Enumera- 
tion ; but these just show the difference between the 
operations themselves, and the results gained by them. 
1 Similar,' ' Equal,' ' T V of,' ' Present, ' Near,' are not mere 
signs of operations performed by the individual intellect. 
We unhesitatingly treat them as characteristics of matters 
which we meet with in the objective world. We find them 
out by combination, comparison and measurement, but we 
treat them as independent of the acts of our individual mind. 
' Present ' may create a difficulty, if we think of it solely 
as present to us ; but it is obviously a relation predicable 
and constantly predicated of objects or occurrences with 
reference to any self-conscious subject. Indeed, all names 
are signs of thinking operations, so that this would be no 
distinction between names like ' equal,' ' near,' and names like 
'warm,' 'painful.' 

But it is true that the inflectional and formative elements 
in question have this much in common with mere signs of 
intellectual acts, that we use them in propositions before we 
make propositions about them ; and that when we come 
to make propositions about them we still have to employ 
them in one form, in order to make propositions about 
their other and abstract forms. And further ; like signs of 
intellectual operations, they cannot exist by themselves; 
they are not intelligible unless put in connection with sub- 
stantive elements. You might say ' " Of" is not " For " ' in the 
sense that a man's legal property is not morally for his sole 
benefit ; but then the related points are supplied in inter- 
preting. The proposition is not intelligible in the same 
immediate sense in which ( Red is not Green ' is intelligible. 

22 Introduction. [introd. 

Thus the formative elements of language are not complete 
names on the one hand, nor mere signs of intellectual 
functions on the other. They are however significant, and 
significant of matters which are capable of being named. 
But the matters or characteristics which they signify are 
such as to presuppose related terms, and to be incapable 
not merely of being, but of being understood, apart from 
those terms. We find these meanings or attributes therefore, 
in the first instance, in explicit dependence on the simpler 
contents which they imply ; and we only find them treated 
as nameable or isolable contents at a stage of reflection 
which can supply the presupposed simpler contents in a 
typical form. Thus their apparently subordinate position in 
the simpler classes of judgment comes not from their being 
so little significant, but from their being so much. They 
indicate, not indeed mere acts of mind, but the realised 
wholes which arise for knowledge through those acts of 
mind. Their names are names for such wholes, and for 
nothing less ; as expressive of a special relation within an 
individual whole they are not names but auxiliaries \ 

It is quite true therefore that the formative elements of 
language imply acts of mind ; but not true that what they 
indicate are mere acts of the individual mind, such as 
Judgment or Comparison. 
Naming vi. So far we have spoken of Naming as involving Refer- 

tinction." ence or Objectification, and of Objectification as involving an 
affirmative or positive content. Are we obliged by these 
conditions to treat Distinction and Comparison as essential 
to the act of Naming ? When we refused to apply the terms 
1 definite ' and ' determinate ' to the positive something 
which constituted the identity that can be named, we did 
so in order to avoid begging the question of distinction 

1 ' Here ' and ' now ' are peculiar. As implying relation to the subject which 
judges they carry their points of application with them even in their first and 
direct use, and can be used as logical subjects even in perceptive judgment ; 
while for instance ' at ' and ' in ' cannot. But ' here ' and ' now ' generalised 
into 'Presence' drop the special relation to the judging subject, and indicate 
a relation to any judging subject. 

introd.] Distinction, 2 3 

and comparison. We felt sure however of one thing, that 
a positive content is what makes distinction possible 1 , and 
cannot itself consist in a mere distinction from something 
else. I am speaking all through of being as it is for know- 
ledge ; not of the ontological, and to my mind, fruitless 
question, how being can be apart from a consciousness. 
What I say is, that we cannot see how the characteristic 
quality of a colour should be supplied by the distinction 
between it and all other colours. And if the process of 
distinction does in fact make us notice all the features 
of something present to perception, this is only because 
contrast, in this case, invests those features with an interest 
which they might equally have obtained in some other way. 

Mere distinction is not the essence of naming. On the 
other hand, distinction is implied in the purpose of naming. 
I do not say that the implication is always apparent. But 
the least reflection, the least practice in the use of language, 
must bring it to the surface. We shall constantly have 
occasion to speak of the interest or purpose which is essen- 
tial to all judgment. And it meets us here on the threshold 
of intelligence. Why do we name ? Why do we refer to 
an identity ? What do we want with a set of signs ? To 
give voice to our positive wishes and feelings, we may reply. 
Doubtless, in the first instance. But this very giving 
voice, this fixing on a something, is selection. It answers 
the question, ' What do you want ? ' and is meaningless 
except as an act of choice. If there was only one thing in 
the world, we should not want a name except to dis- 
tinguish between having it and not having it ; or if we 
wanted no distinction, we should want no name. And 
when we use a name, we ipso facto select, because we omit ; 
and we omit on a plan and with grounds, because a purpose 
guides us in selecting. 

Therefore I should state the relation between naming 
and exclusion or distinction, as follows. Reference or 
Objectification, as represented by Naming, carries Distinc- 

1 Cp. Lotze, Logik, sect. n. 

24 Introduction. [introd. 

tion or Exclusion with it formally. I do not mean 
externally or explicitly, but just the reverse. The act of 
Naming is in the abstract an act of selection, though we 
may not at first find it out. It is therefore selective or 
exclusive in form, but is not so materially, in any special 
relation, till we use it for that purpose. And how soon this 
happens, how soon and how far a material value is actually 
given to the implied element of exclusion, is a question 
rather of anthropological psychology than of logic. In 
the very beginnings of human thought (which I take as 
equivalent to thought aided by speech) it may be supposed 
that the sense of distinction would be chiefly represented by 
the effort to identify and fix under a name, and by the 
feeling of success when the desired result was attained by 
such means. It is clear that such effort or success would 
represent a rudimentary work of distinction, which combats 
the difficulty of fixing the content and of finding and 
adopting the sign. Or if the sign-system grows without 
perceptible effort on the part of individuals, there is still the 
interest to which I have alluded. The distinction of man 
and woman or meum and tuutn must, one would think, 
invest some contents with negative determination from the 
very first. 

On the other hand, even our reflective thought is per- 
plexed when its attention is first directed to the mutual 
implication of very familiar facts, which seem to have inde- 
pendent being because so familiar. The essence of objects 
in space may not be in distinction ; we certainly however 
tend to underrate the importance of distinction in knowing 
them. And when we come to negations such as those 
implied in consciousness or morality, for instance mind 
and matter, sin and the law, the degree in which essence 
seems to consist in distinction surprises us at first. Distinction 
then is formally involved in Naming; but the degree in 
which it is realised as distinction between ' this' and a definite 
other, and as essential to the character of ' this,' is not deter- 
mined by the mere use of a significant sign. It may not 

introd.j Essentially relative! 25 

be so realised at all. And when it is so realised, it involves 
logical forms which go beyond the Impersonal or other 
nuncupative Judgment ; forms such as negation, disjunction, 
and classification. 

There are indeed facts which are such as to be essentially 
relative (i<ad' avrd irpos tl) a pregnant conception of Aris- 
totle. And obviously all facts partake progressively of this 
character as they are united with the whole of knowledge, 
and as, in this process, their centre of gravity, so to speak, is 
shifted outside them by their connection with larger systems. 
We can scarcely understand a curve except as distinguished 
from a straight line ; nor sin except as distinguished from 
a good will. Nor can we know even red light or violet 
light scientifically without including in the conception of 
each its wave-length and degree of refrangibility or place 
in the spectrum a disjunctive knowledge which involves 
a number of precise reciprocal distinctions. As thought 
grasps more of its object, the object takes more of this 
coherent character. And in an object thus coherent, it 
may seem that distinction or negation takes the place of 
affirmative nature. Straight is the line which is not 
curved. Sin is the will which is not good. Red is the 
light at the other end of the spectrum from violet. 
Here we are in the region of the complicated contents 
described above as relations. Distinction has here a 
value which it had not before, but it is not mere distinc- 
tion or mere negation. The distinction is valuable for 
its positive ground, and the negation for what it affirms. 
The point is not that the essence of a fact can be 
given by mere distinction, but that positive matter finds 
it necessary to take the shape of distinction and negation. 
I shall return to this subject in treating of negation and 
disjunction. The distinction from straight is the essence 
of curve, only because or as far as the positive spatial 
nature of line and direction is involved in ; straight,' and this 
same spatial nature is also involved in the opposite curved. 
It is not really that ' Not straight is curved/ but that ' What- 




and Com- 

ever is a line and not straight, is curved.' It is the nature of 
space, as known in line, and in constant and varying direc- 
tion, that forms the positive content of both determinations. 

Thus it is never true in the plainest sense that a thing or 
matter of fact has its essence in mere distinction from 
another ; but it is true, as we shall see more fully, that all 
reality is so entangled and interwoven, or rather is so 
coherent in each of its several regions, that in mastering the 
positive essence of one fact we are forced to master that of 
many more, all of them being branches of the same stem. 
Even in the simplest cases there is at least an element of 
content common to the facts distinguished, like the stem 
up to the parting of the branches ; and every distinction 
made between them has this at least for its positive content, 
as in distinguishing red from violet we imply that both are 
light. But no doubt in more intricate cases, the alternative 
or alternatives may be essential to their subject ; and in that 
case the metaphor of the tree breaks down, for the nature 
of the whole is such that one branch perhaps cannot be seen, 
or perhaps cannot exist, apart from the perception or the 
existence not merely of the stem but of the other branch. 
Still we must think of the positive nature of the whole 
revealing itself in this peculiar form (say the nature of a 
moral being revealing itself in the good and bad will) ; mere 
distinction or negation is no characteristic at all. 

Distinction then is involved in the purpose and essence of 
naming, but primarily as a consequence. Meaning, or the use 
of names, is never mere distinction ; though proper names 
are used for the sake of mere distinction, and so with no 
care for positive meaning except as subservient to that end. 
And though in the deeper grasp of reality Distinction, 
Exclusion or Negation comes to be an active and prominent 
property of fact, yet this exclusion depends for its value 
always on its positive ground or motive, and never, as such, 
constitutes the essence of anything. 

vii. And what is true of Distinction is true of Comparison, 
or rather, as I shall use the terms in future, of Identification. 

introd.] Comparison, or Identification. 27 

Formally, in the light of analysis, and in respect of purpose 
and interest, to use or give a name is Comparison. For it 
is identification, the establishment of an identity which 
holds good in spite of differences. We may illustrate by the 
German word ' Vergleichung,' which is usually rendered 
' comparison,' and which seems to be used in logic (I am 
not speaking philologically) to mean the establishment of 
a ' Gleichheit ' or immediate identity between the terms 
compared. This applies cannot but apply to the use of 
names as we have described it. But if we take Comparison 
at the other extreme of its meaning, which ' Vergleichung ' 
shares with it, we must say that it is a distinct reflective 
operation, which presupposes naming and is not implied in 
naming. Comparison par excellence is a process which 
starts from the content of recognised names, and reacts 
upon it with a view to the interest which may have provoked 
the operation. Ultimately as a scientific method, it involves 
measurement, and is the instrument of classification ; where- 
as the use of names must be prior to number or measure, 
and classification as a method of science arises so late that 
its genesis is almost within our ken 1 . 

It would be easy to say, in the tone which I deprecated 
above, that Identification as a method of science pre- 
supposes Distinction, and therefore is a process naturally 
later than Distinction, and not to be looked for concurrently 
with the latter in the earlier stages of knowledge. But this 
would be merely a commonplace blunder. It would be as 
easy to show that Distinction presupposes Identification, as 
that Identification presupposes Distinction. Before you can 
distinguish colours as red and green, you must identify 
them as coloured surfaces ; and before you can identify the 
surfaces in respect of colour, you must distinguish them as 
separate areas in space. We can come to no good result in 
this way. We are merely pointing out, not any special 

1 In Western thought, it was probably first analysed and its import pointed 
out by Plato. In practical life it must have arisen in the earliest society by the 
effect of social rules ; see above on distinction. Exogamy is an instance of 
an early custom which operates through classification. 

28 Introduction, [introd. 

relation between Distinction and Identification, but that 
every level of reflective observation presupposes a previous 
level on which it improves. How do we begin then ? It 
may be hard to say how matters get into consciousness, but 
all that is in consciousness seems to present both difference 
and identity. And we shall find how closely they are 
connected, and reveal the true relation of Distinction and 
Identification in the germ of knowledge the act of Naming 
if we look closer at the nature of Comparison itself, taking 
this as a process which may end either in Distinction or in 

If, in order to effect a comparison, we trace two shapes, 
say the shapes of two leaves, one upon the other, it is 
clear that we shall have a repetition at every minutest 
step of what takes place in the act of naming. Coincidence, 
deviation curve and straight jagged or uncut notched 
or entire ; the discrimination of universal characters like 
these, with, if worth while, accurate measurement of differ- 
ences, will mark the process as it goes on. In respect 
of each of these points we may infer an identity or 
a distinction ; we express an identity by a single judg- 
ment, either 'The outlines coincide' or 'Both outlines are 
slightly serrate ; ' a distinction either by the single judgment, 
1 The outlines are different/ or by the two judgments, One 
outline is serrate and the other simple.' We should notice that 
if any portions of the two outlines absolutely coincide, we 
can only predicate identity of them within that 
portion by bearing in mind the ideal continuity 
of that bit of line E C with the two differing out- 
lines E C F and E C A. If we leave this out 
of account, judgment and identity disappear. 
Hence it seems to follow that complete comparison must 
always resolve the terms compared, in the respect in which 
they are compared, into cases under a universal, or differ- 
ences within an identity. Identity without difference, or 
difference without identity, destroy the meaning of com- 
parison. It is for this reason that the single judgment will 

introd.] Complementary aspects. 29 

not contain a complete comparison. We shall see that 
a disjunctive form is really required. But it is true that the 
conclusion in these processes moulds its result into apparent 
opposition to its starting-point, or rather, causes us to read 
into the starting-point the complementary aspect to that 
which is proclaimed in the result. This is simply because 
the result is a modified form of one element in the starting- 
point ; of the identity if it is an Identification, of the differ- 
ence if it is a Distinction. The complementary element is 
thrown into relief by the explicit exhibition of the new 
determination, so that Difference always seems to be predi- 
cated of Identity, and Identity of Difference. But really 
the judgment has done nothing more than to develope further 
either the identity or the difference of the datum. ' X and Z 
are like ; ' here we take X and Z as distinct objects, though 
we know well enough that if they are like, they were com- 
parable. ' X and Z are different ;' here we take X and Z as 
instances of some class or rule and so far identical, though 
we know that if they are different they were distinguishable. 
'" Sorrow" and " Sorry" have quite different etymologies.' 
1 " Sorrow " and " Sorry " have the same meaning.' The former 
proposition assumes sameness of meaning, in spite of which 
it asserts difference of etymology; the latter starts from 
a difference of form, perhaps intensified by a difference of 
etymology, in spite of which it asserts identity of meaning. 
And yet the former also treats the words as two, and the 
latter as prima facie the same in their significant part. 

I do not think that distinction can be effected except by 
developing differences which are presented, or identification 
except by developing an existing identity. But of course 
either element may be very faint at first. It is of no use to 
say that we may be artificially set to search for distinctions. 
No motive will help us in science unless it guides us ; and if 
it guides us to a distinction, then it contains the distinction 
in germ. The same is true in searching for identities. Thus 
it would be hopeless to distinguish the two sodium lines in the 
spectrum while they look single as a small instrument shows 

30 Introduction. [introd. 

them. And we could never distinguish Ricardian rent from 
common farmer's rent (e.g. including interest of capital) 
except by pressing home the differences which are given 
with, and in, the two kinds of cases. This, like many con- 
siderations in logic, will help us to understand the childishly 
tardy progress of early intelligence, and the cumulative 
rapidity with which knowledge generates knowledge. 

Naming then implies some degree of Distinction and 
Identification. These two processes might, as we have seen, 
conveniently be included under Comparison. But Com- 
parison, Identification, and Distinction, as involved in 
naming, are not the developed methods of which I have 
spoken 1 . In developed knowledge their organa are measure- 
ment and counting, in which it becomes mere pedantry to 
separate Identification from Distinction 2 . I shall return to 
this point in speaking of the value of Judgments, and shall 
there treat the earliest distinct judgment of Comparison as 
the transition to number and measurement. But the key- 
word of mere naming is Recognition ; and this is the limiting 
purpose of all functions qua subservient to naming. And as 
i regards the affinity between Distinction and Identification, 

they are obviously two sides of the same process, and it 
is idle to ask which came first. So far as we can see, Con- 
sciousness, or at least Intelligence, must begin with both. 
Concept . 6. Enough has already been said to make clear my 
ment . S " general view of the growth of logical functions. While I 
would spare no pains to ascertain the precise order in which 
and differentia with which logical activities make their 
appearance, I have never been able to doubt that the central 
function of the intellect, I would even say of consciousness, 
is one from beginning to end 3 . In speaking, therefore, of 

1 See further Bk. II. ch. i. on ' Immediate Inferences.' 

2 I mean that it is pedantic to restrict measurable identity to the case of 
absolute equality, but that if you do not, you must admit a degree of distinction 
to be present in all cases. A distance of 400 miles and another of 400 miles 
1 yard are as we say ' the same to a yard' ; and this is the true way of putting it. 

3 Cp. Bradley, Principles of Logic, p. 455 ff. Mr. Bradley's views on this 
question have influenced mine, but rather in the way of moderating than of 
suggesting or intensifying the view adopted in the text. 

introd.] Succession of logical activities. 31 

the connection between impressions and ideas, and again 
between ideas or concepts and the judgment, I am obliged 
to reject the easy partition into distinct operations which 
finds place in many text-books. More especially, I cannot 
at all follow Lotze in his treatment of this connection, and 
I select his work, as probably the most permanent in value 
of those which adopt these views, to comment upon when 
comment is necessary. 

As I read Professor Lotze, the act of Naming coincides 
with that shaping or moulding of an impression which is 
required to convert it into an idea, as a stone requires 
shaping to make it fit for use in a building. And then, 
subsequently, the ideas so shaped are fitted together, and 
the result, I suppose, is a concept ; while it is not till the 
simpler concepts come to be combined that the judgment 
takes its rise. Ideas, it will be observed, are thus subse- 
quent to impressions, concepts to ideas, and the judgment 
is subsequent to the simpler concept. 

It is worth while to notice the nature of the analysis by 
which this account is defended. Impressions must be 
shaped like stones before they can be fitted together * 
Judgments must presuppose at least simple concepts* 2 , 
because judgments consist of concepts, and if such con- 
cepts presuppose judgments, where are the concepts to come 
from which -make up these latter judgments ? It is hard 
to think that such arguments as these really expressed 
Lotze's mind ; they must rather have resulted from over- 
eagerness to present a perfectly clear arrangement to his 
readers. The thought of a germ which unfolds differences, 
of the elementary sensation as already containing, in the 
features which make it a state of consciousness, rudi- 
mentary distinctions which are shadowy at first but receive 
form and fixity by degrees, such conceptions seem at 
once to destroy the application of arguments drawn from 
mechanical processes. If metaphors are indispensable, we 
should rather call to mind such processes as the formation of 

1 Lotze, Logik, sect. i. 2 Ibid. sect. 8. 

32 Introduction. [introd. 

structure in an embryo, as the separation of a double star 
by successively higher powers of the telescope, or indeed 
as the discernment of features in a distant landscape which 
prolonged attention even without optical assistance has the 
power to effect. 

And, though the suggestion is hazardous, I cannot but 
think that Lotze allowed himself to confuse change as pro- 
cess in time with the rectification of error in knowledge *. 
There is nothing whatever in the concept or idea, as Plato 
thought of it, to interfere with its expressing the laws of 
process in time. The constitutive equations of curves, 
read in connection with the law of gravity, have, so far as 
we can see, precisely fulfilled one of the grandest aspirations 
embodied in Plato's view of science, the establishment of 
the true laws of motion as they are in general, and not 
solely or specially for the heavenly bodies 2 . And these 
equations are the instance which Lotze gives of the highest 
order of concept 3 . Such a concept or idea embodies the 
very essence of process in time, or change. It is true that 
change is also a principal vehicle of indications that our 
concepts are erroneous, and therefore often requires them 
to be changed, but this is not because the concepts are 
concepts, but because they are wrong. It is wholly an 
illusion, founded I presume on the doubtful idea that pre- 
dication involves reference to time, or even that the judg- 
ment is a transition in time, to suppose that the judgment 
as such can represent change or Becoming,' while the concept 
cannot. To make this in the least probable it would be 
indispensable to confine the judgment to narrative judg- 
ments which use tense, and thereby to abandon all scientific 

I cannot but think that the reasons alleged by Lotze for the 
transition from Concept to Judgment are wholly visionary; 
and merely conceal the unreality of the entire arrange- 
ment which made such a transition necessary. There is 

1 Lotze, Logik, sect. 34. 
3 Plat. Republic, 530-1. 3 Lotze, Logik, sect. 117. 

introd.] * ytidgment and its parts. 33 

truth, indeed, in the remark that the judgment reconstitutes 
the concept with a reason ; but is there any possibility that 
the act which reconstitutes the concept is fundamentally 
other than that which constituted it at first ? 

I will summarise the criticism which I think essential 
on the whole point of view indicated by the ordinary succes- 
sive arrangement, and especially by Lotze's form of it. 

If a Sensation or elementary Perception is in Conscious- 
ness (and if not we have nothing to do with it in logic) it 
already bears the form of thinking. I will not say that it is 
a rudimentary judgment ; but it is certainly an act, for it 
is a change within a percipient subject; it has identity in 
itself, or it could be nothing for consciousness, and differ- 
ence, or it could not have identity; and it stands out 
against other elements of the momentary consciousness in a 
way that approaches to an attribution. An Impression or 
sensuous idea becomes a logical idea when it is fixed and 
referred ; fixed and referred if we like to say so by 
receiving a name, though this is rather a sign of the act 
than the act itself. We have here the explicit form of 
judgment given to what before must have been a mere 
actual extension of sensations by idea, depending on a 
general identity, but not consciously referred to an identity 
other than the psychical image. 

Judgment is not, in relation either to impressions, ideas 
or concepts, a mechanical combination of parts which 
remain outside each other. It is an expression perhaps 
at bottom the only expression of the unity in which 
consciousness consists. I do not mean that it is nothing 
more than an idea or impression ; but I incline to think 
that it is better described as an idea or impression writ 
large than as a combination in which ideas or impressions are 
units. Judgments may contain complex ideas, but every 
Judgment qua Judgment exhibits the content of a single idea. 
Ideas and Impressions, as I have tried to show above, are 
not found lying apart as words lie on a page, although, by 
a reflective abstraction, we can regard them as so lying 

VOL. I. D 

34 Introduction. [Introd. 

apart, and when thus regarded they form the world of 
meanings or of objective references the identities symbol- 
ised by logical ideas. 

We have then Judgment or some analogous operation of 
Consciousness, from the first 1 ; and in naming and all subse- 
quent operations we certainly have Judgment. What we are 
watching all along is the development of an act, a function. 

Thus Judgment and Idea go pari passu. An Idea is not 
presupposed by Judgment anymore than vice versa. And 
it is, as I have explained, an extraordinary confusion to 
account for the advance from concept to judgment by the 
inability of the concept to represent change. 

And indeed the whole question of advance from concept 
to judgment is meaningless to me, for I think of the concept 
as existing only in the act of judgment. I have tried 
above to explain the deception which language practises 
on us in this respect. The question is not easy, and is 
all-important. I shall therefore return to it for a moment. 

If a man were to say in our presence ' The Sun ' and no 
more, we should either suppose that he meant ' The Sun is 
visible,' or, if circumstances excluded this interpretation and 
furnished no other, we should turn upon him sharply and 
ask, ' Well, what about it ? ' This implies that the words 
have conveyed a meaning to us, but that the meaning is 
incomplete. I will speak of the second point first. It may 
be said that our impatience of the incompleteness of the 
thought is ethical and not logical ; that it arises from 
annoyance at the waste of an intellectual effort, or at the 
interruption of other thoughts, seeing that nothing is to 
result from it ; and not from any inability to think the 
thing ' sun ' by help of our idea of it, without judging. 

This explanation would have much truth, and only needs 
pushing further. We should in such a case miss the 
ethical purpose which all thought implies. But this defect 
would have a logical side, which would be this; that we 

1 Cp. Bradley, p. 455 ff. And see below, Book II. chap, i, on the lower 
limit of Inference. 

introd.] What is a tentative judgment f 35 

should be started upon an intellectual exercise not only 
objectless, but also and for that reason endless. Thus the 
meaning is incomplete because undetermined. We are left 
to traverse an indefinite series of judgments. 

And yet (I return to the first point) a meaning has been 
conveyed. In what shape does it exist ? The natural 
answer would be that an incomplete meaning must exist in 
the shape of questions or suggestions of tentative judg- 
ments. But a tentative judgment lacks, it would seem, the 
differentia of a judgment. It does not assert, it does not 
claim truth. Therefore we have prima facie in the idea 
or conception something that will not go into the form of 
the judgment. An idea in this stage seems to be in a 
position corresponding to that of a relative or dependent 
clause or clauses without a principal clause; a form of 
language which certainly can exist, but which has not an 
independent right to existence. Or it may be taken as 
corresponding to a question. ' The sun, around which the 
planets revolve, which is hot and bright ; ' The battle 
lost or won ? ' These instances give different cases. In 
the former the attributes are all constant, and we might if 
we chose say that we first judge, affirm certain attributes 
of a thing, and only leave it undecided what attribute is in 
question here. If this was so, we should have something 
like a disjunctive judgment. In the latter case, that of the 
question, the form of sentence is considered absolutely to 
exclude a judgment, although we have assumed the material 
for a disjunction to be furnished by the prevalent interest 
of the moment. What is the thought corresponding to a 
question? I do not find any sufficient discussion of this 
subject in the logic books 1 . Is a question a peculiar act 
of thought at all, putting language aside? The test for 
this is to see whether we can genuinely ask ourselves a 

1 Cp. Bradley, Principles of Logic, pp. 13-14. His treatment is definite 
though brief, and I cannot agree with it. I cannot think it possible that the 
content of a doubt or negation should be the same as that of the corresponding 
affirmation. Cf. Sigwart on the Question, Logik, i. 191. 

D % 

36 Introduction. [introd. 

question, or whether it is, like a lie, only a form of speech 
which has the object of producing a certain effect on others. 
I am disposed to doubt whether we can interrogate our- 
selves. It appears to me that a question directed to one^ 
self for information which one has is always rhetorical, is 
a concise summary of the interest which the information 
has for us. But we too often have to ask ourselves questions 
which we cannot answer, and know that we cannot answer. 
I do not see how these, again, can be genuine questions. 
While in the former case we know the answer already, in the 
latter we know that there is at present no answer possible. A 
question addressed to another person in such a case, i. e. know- 
ing that he cannot now answer, has not the differentia of a 
question ; it is a mere guide to him as to the information 
which we wish to possess, a memorandum for future use 
when he may have the information. But, if we are speak- 
ing with ourselves, this leads to the former ground of 
rejection ; the question becomes, as before, merely rheto- 
rical. And thus there is not even a prospect of genuine 
self-questioning; to treat oneself as another may react 
powerfully on the imagination, but is impossible in strict 

Thus a question cannot be an act of thought as such, 
just as a lie is not, and for the same reason, that it is not 
an attitude that the intellect can maintain within itself. 
A question is not merely doubt ; nor merely doubt plus 
the knowledge that the doubt can be resolved in a particu- 
lar way. It is a demand for information ; its essence is to 
be addressed to a moral agent, not ourselves, in whom it 
may produce action. It is closely analogous to the impera- 
tive, which also cannot be addressed to ourselves except by 
mere metaphor. Thus to say that the mere mention of a 
name leaves us questioning or fills us with questions, is not 
to say what it does for thought. 

I suppose that the thought, on which a question is based, 
must always partake of the nature of disjunction. Where 
the interest lies wholly on one side of the alternative this is 

introd.] Question and Disjunction. 3 7 

hardly noticeable, 'Are you going to see Hamlet?' We 
scarcely think of the possible negation as an alternative at 
all, but rather as a bare nothingness, a rejection of the idea 
proposed in the question. A more difficult case is ' How 
much did you give for that horse?' In this case, as in 
asking 'Where' or 'When?' we assign the general principle 
of the Disjunction under which the answer is to fall, instead 
of selecting an alternative and demanding information 
about it. 

I should therefore be inclined to think that when a man 
says ' The battle ' and then stops, and we ask ' Lost or won ? ' 
our thought is really a disjunctive judgment with reference 
to which we express a desire for an action ab extra that 
will enable us to accept one of the alternatives. The same 
result follows if we describe an act of thought as doubting. 
It is impossible to doubt without knowledge, and a definite 
doubt, apart from a moral or religious sense of the term 
(for a degree of failure of will may pass for doubt in these 
spheres) is unquestionably a disjunctive judgment. 

And if now we return to the case of the sun and its 
constant attributes, we may find that a similar account is 
possible. The speaker has uttered what is the equivalent 
of a dependent sentence; he sets us judging in distinct 
affirmations about reality which form our resources for 
estimating what he can mean (or suppose we judge about 
his mind, it is no less true that we judge), and the in- 
definite series of these affirmations may be treated as an 
imperfect disjunction. It makes no difference whether we 
conjecture as to his meaning or as to the fact which may 
underlie it ; whether we think ' He either means the sun is 
just visible, or that it is hot, or ,' etc. ; or again, simply, 
' Either the sun is just visible or,' etc. 

Such judgments are prima facie substantive or indepen- 
dent judgments. But if it is our express purpose to regard 
what has been communicated as nearly as we can in the 
light of a mere idea, mere concept, or mere possibility, then 
we must be taken to affirm the universal meaning which 

38 Introduction, [introd. 

pervades these judgments to be true of Reality under 
specific but unknown conditions, a mode of affirmation 
which we shall find to be the essence of the problematic 
judgment. Such a point of view as this is rendered inevit- 
able, in the case supposed, by the absence ex hypothesi of 
any ground for restricting our affirmation to any special 
element of the universal content, unless, as in the example 
of the question about a battle, a determinate or partly 
determinate disjunction is provided by the context. A 
mere idea then as distinguished from a judgment, but con- 
sidered as the mere meaning of a name or as an objective 
reference in the world of meanings an isolated idea is 
the content of a reflective problematic judgment, and is 
referred to reality as true under unknown conditions or 
among unknown alternatives. But every idea has its 
existence in the medium of judgment. 

The judgments which embody ideas may have many 
degrees of unity. The identity which pervades a set of 
judgments may be quality, thing, or complex attribute. 
When the identity is a quality the judgments in which it 
appears are but slightly connected, and one member of the 
group will not necessarily be accompanied, opposed, or 
conditioned by any of the others. In the case of groups 
of not very coherent attributes, such as form concrete things 
in space, the result is exceedingly curious, and it is very 
doubtful whether the judgments into which the thing enters 
should be treated as single rather than as multiple. For 
the judgment which is made is often related to the others 
which the identity binds to it, not as consequent to con- 
ditions or grounds, nor as conclusion to premisses, but as if 
joined with them either by a copulative or even by an 
adversative conjunction. ' The strongest men were afraid 
of him,' i. e. The strongest men, though much stronger than 
him, yet were afraid. Or, The strongest men were very 
much stronger than him ; and yet, etc. Or, again, The 
Venus of Milo is in the Louvre ; in this any number of 
judgments may be supplied out of the subject, and linked 

introd.] Petrified Concepts. 39 

by a mere ' and ' to the one given. There are all degrees 
of conjunction ; it is well known that even ' and ' may carry 
either adversative or inferential meaning. But where it 
carries pure conjunctive or pure adversative meaning, there 
must be a question how far the proposition represents a 
single judgment. It is from this ambiguity that the judg- 
ment is freed by assuming the hypothetical form. 

To analyse these degrees of unity here, under the head 
of the concept, would be superfluous. The whole work 
of logic is to depict them in the order of judgment and 

It should be mentioned that there is unquestionably a 
reaction of judgment on the actual image or appearance 
presented to perception. No doubt, all arrangement in 
space has been learnt, but I take it that the disposition of 
points on surfaces perpendicular to the axis of the eye, even 
if a result of interpretation applied to feelings of motion, is 
when once learnt an inevitable process, for every detail of 
which there is a special distinct sense-stimulus. On the 
other hand, in the perception of depth it appears to me 
that we have a generically different case. The interpreta- 
tion of certain dispositions of colour, and of certain feelings 
in the ocular muscles, to mean ' if I want to touch that 
point, I must put my arm out as far as I can ' this would 
cause me no surprise, and would simply be knowledge 
brought to bear on perception, just as it is when certain 
appearances indicate that one has food or poison before 
one. What is noticeable in the case I now speak of, is 
that the interpretation reacts on the image, that we seem 
to see depth exactly as we see height and breadth ; and 
that, in learning to draw, the counteraction of this inter- 
pretation, and the reduction of objects to their places on a 
plane surface is a matter of extreme difficulty. The solid 
images in which a mere interpretation is thus made visible 
as a fact, do realise the popular notion of what I might call 
a petrified concept, a group of attributes and relations 
which stands still to be looked at. Ultimately, however, 

40 Introduction. [Introd. 

even this petrified concept is a judgment a perceptive 

I will recapitulate our results so far : 

i. Naming, or the appropriation of fixed signs for mean- 
ings, always marks a first step in the thought which acts 
so ; scientific naming e. g. marks a first step in a region 
of science, though a late stage in the history of the human 

ii. The formative elements of language are significant, 
but qua formative elements are not names, because their 
meaning is incomplete without that of other elements. 
At a later stage of reflection names are assigned to their 
entire significance, that is, to the classes of complex wholes 
which they imply. 

iii. A name has meaning only in a sentence or by sug- 
gesting a sentence. The sentence is the significant unit of 
language. This is most easily seen in ancient speech, but 
is equally true of modern and analytic tongues. Depen- 
dent or appositional sentences can enter into names. It is 
probable that the thought corresponding to a sentence is 
always assertory. 

iv. Naming involves Objectification the treatment of 
that which receives a name as an object of knowledge, as 
recognisable, that is, in a world which exists for all thought 
as such, and is not dependent on the thinking of the indi- 
vidual mind. 

v. Objectification involves being as a positive somewhat 
on the part of that which is to be treated as an object of 
knowledge, but this does not amount to the exhibition of a 
'definite' and 'determinate' nature. 

vi. ' Being as a positive somewhat ' includes in a formal 
sense being known by Identification and Distinction, which 
are the two sides of Comparison. But as processes of real 
or material import, these methods presuppose number and 
measurement, and are posterior to fixed names. 

vii. That which is named is always an identity in differ- 
ence, and must disappear if either element is neglected or 

introd.] Work of the individual Mind, 41 

removed by abstraction. This is illustrated by the relation 
of names to sentences. 

viii. Every name refe?'s to such an Identity treated as 
an object of knowledge, whether thing, quality, or relation. 

ix. The meaning of every name is in what it refers to or 
is meant to mean ; but this is represented to the individual 
intellect by the significant idea which the name causes it to 

x. An idea or concept is not an image, though it may 
make use of images. It is a habit of judging with 
reference to a certain identity. 

xi. There is no correspondence between Concepts as such 
and Quiescence, or between Judgments as such and Change. 
As the fundamental form of Knowledge the Judgment 
tends to overcome change, and to view phenomena sub 
specie aetemitatis, and is in this respect at one with the 
Platonic ' forms.' 

xii. The grades of unity and complication of ideas and 
concepts are the same as those of judgments and argu- 

xiii. The relation of the concept as representative of the 
meaning of a mere name, to the assertory judgment, is 
illustrated by the relation of the dependent sentence and of 
the question to the assertory judgment, and depends upon 
the possibility of making the identity in a group of judg- 
ments the content of a relatively reflective judgment. 

7. It will be observed that having spoken at first of what Logical 
I may call the logical meaning of names, i. e. of their ^j"^"/ 
reference in the general world of thought, I have digressed mind, 
in the last few pages into discussing the act of judgment 
by which the individual mind realises that meaning. The 
purpose of this was to show that the acts set in motion by 
the name and by the proposition were the same, and there- 
fore the logical function of these forms could not be gene- 
rically different. 

But before further considering the logical meaning, it 
will be well to say something on the relation between the 

42 Introduction. [introd. 

universal or logical meaning and the act of the individual 

Logical meaning we have treated all along as taken to 
exist in the world of meanings, the world which is common 
to thinking beings as such. Not merely London and Mont 
Blanc, but virtue, redness and pleasure, have their being in 
this objective world of meanings. And yet the meaning 
which on the one hand belongs to a world independent of 
the individual peculiarities of our thought and perception, 
is on the other our meaning. It is dependent on our 
private experience and our private intellectual endowment 
in two ways. 

First, the psychical ' ideas,' the images which our mind 
generates from moment to moment and which never recur, 
are only such as our memory, conjoined with the sugges- 
tions present at the moment, will supply. Mr. Bradley has 
well explained how, as images in our minds, these are not 
ideas in the logical sense, not significant, not meanings. 
We use these images, make them starting-points of thought, 
treat them as containing approximations to what we 
mean; we direct ourselves to omit parts of them, or to 
note that they require weakening or intensification. We 
may illustrate this by the way in which we attempt to 
communicate a qualitative impression ; but it is only an 
illustration, because we cannot employ as an instrument of 
communication a particular momentary psychical image ; 
it is not transferable, not capable of being reawakened 
with precision by language in another individual mind, nor 
in our own. We must employ then an image which is 
already so far universalised as to be subordinate to a mean- 
ing ; but which may be diverted from its original meaning 
and applied to another in a way that illustrates the em- 
ployment of a psychical image. ' Not quite sky blue, but 
a little darker ;' ' Between pleasure and pain ;' ' A baritone 
is in quality something like a tenor, though with points of 
resemblance to a bass.' 

Now though, after this fashion, we can deal freely with 

ixtrod.] Reference and Content. 43 

our particular psychical images, and make them do duty in 
very various contexts, yet there are limits to the modifica- 
tions which can be effected in them. To take a well-worn 
instance, we cannot suppose that a man blind from birth 
can ever make judgments involving the quality of colours, 
although he can obviously learn the mathematical theory 
of undulation and refraction. But the whole region of 
particular psychical occurrences, immediate impressions of 
colour, which are made use of in referring to the recognised 
colour-system, would simply be absent from his mind. 
Structure, on the other hand, involves mainly relative 
conceptions, such as movement and position, in which the 
nature of the particular images employed is indifferent ; 
or, if we mean the structure of an argument or institution, 
the notions required are such as condition and consequent, 
function and purpose. Structure therefore can be repro- 
duced by any intelligence furnished with the chief*capacities 
of an intelligence as such. 

But, secondly, ideas, even in the sense of meanings, are J 

on one side individual and peculiar. The intellect, at least 
the individual mind of which we are now speaking, does 
not move wholly in the objective world of meanings to 
which its acts bear reference. In extreme cases Content 
and Reference are in contradiction ; in less extreme cases, 
in veiled contradiction. ' Oh I see, my dear sir/ said 
a theological disputant, 'your God is my Devil! Both 
parties had made the same reference, viz. to God ; neither 
took what he was speaking about for an idea merely in his 
mind ; but nevertheless, in making the reference, each of 
them had employed a peculiar and special act of thought, 
determined by his own intellectual conditions and history. 
The opponent in the dispute maintains that your reference 
is inconsistent with your content ; that one or the other 
must be wrong. But the possibility of conflict is gone if 
the reference of both disputants is not the same, and the 
retort quoted above is an ironical suggestion of a basis 
of agreement on the score of different reference. The 

44 Introduction. [Introd. 

antagonists refer to, or mean to mean, the same thing, but 
they cannot bring their notions of it into agreement. 

If we go lower into mere quality we obtain good illus- 
trations of the line between meaning and psychical idea. 
It is possible, on certain assumptions which do not concern 
us here, to compare some of the colour-perceptions of 
individuals, and it appears that there are various degrees 
of sensitiveness to red light. Now if we take a case, not 
of absolute red-blindness, but of over or under-sensitiveness 
to red light ; we see that the eye which is thus abnormal 
can produce, presumably, all the images which the normal 
eye can produce, excepting only the very weakest in 
the one case and the most intense in the other. But 
these, as we rarely meet with or think of them, we may 
neglect. Now the mind of a man whose eye is thus 
abnormal has the same furniture of images as our own, but 
the meaning in each external reference in which they are 
used must always be slightly different from ours, though 
such differences pass undetected in common life. If I 
speak to him of the red of a Doctor of Divinity's hood, 
he may indeed represent it to himself by any shade of red 
which springs to his mind's eye ; but he will mean a weaker 
or a more intense colour than I mean. In this case the 
abnormal condition has not interfered (as in absolute 
blindness) with the supply of images, but only with the 
occasions on which they are produced, and therefore with 
the meaning attached to each external influence, to each 
red object. 

This paradox that in using names we refer to matters 
as independent of our individual thinking which in this very 
reference are only represented to us by an act of our own 
individual mind, certainly inadequate and possibly contra- 
dictory to the reference this paradox is inevitable if we 
maintain the ordinary line between the mind and the 
world. No doubt the reference demands some one correct 
or at least recognisable element of meaning, or else we 
should set down the name employed as a mistake, and thus 

introd.] The World as a Construction. 45 

if the reference contradicts the content, the content must 
also contradict itself. But this does not alter the fact 
that what we refer to as independent of our intellectual 
act exists for us when referring to it wholly in that 
intellectual act. 

An effort of imagination might help us to see the real 
nature of this paradox. We might try to think that the 
world, as known to each of us, is constructed and sustained by 
his individual consciousness ; and that every other individual 
also frames for himself, and sustains by the action of his 
intelligence, the world in which he in particular lives and 
moves. Of course such a construction is to be taken as 
a re-construction, a construction by way of knowledge 
only ; but for our present purpose this is indifferent. Thus 
we might think of the ideas and objects of our private 
world rather as corresponding to than as from the be- 
ginning identical with those which our fellow-men are 
occupied in constructing each within his own sphere of 
consciousness. And the same would be true even of the 
objects and contents within our own world, in as far as an 
act or effort would be required to maintain them, of the 
same kind with that which was originally required to 
construct them. We should know that correspondence 
implies a degree of identity, but also that every degree 
from mere correspondence upwards had to be won and 
justified by intellectual work ; the onus, so to speak, of 
establishing it would be thrown on the intellect ; and the 
progressive coincidence of our separate worlds would be 
the reward of knowledge. The moral of such a view is 
not a bad one ; for it places the solidarity of mankind in 
the intellectual life. 

Thus the paradox of reference would become clearer. 
We should understand that we refer to a correspondence 
by means of a content. We should soften down the 
contradiction of saying that a name to meet which we have 
and can get nothing but an idea, nevertheless does not stand 
for that idea but for something else. We should be able 

46 Introduction. [introd. 

to say that the name stands for those elements in the idea 
which correspond in all our separate worlds, and in our own 
world of yesterday and of to-day, considered as so corre- 
sponding. Even when we say, taking the most subjective 
of feelings, ' Pleasure is the accompaniment of activity,' we 
refer to pleasure as a point in which all separate worlds 
correspond ; which occupies the same relative position in 
all the worlds which are framed by the consciousness of 
individuals, or, what is technically the same thing, a constant 
position in the world framed by our own. But we should 
not pledge ourselves to any special degree of correspondence 
or of identity resulting from comparison ; only to the bare 
justifiability of the reference. This suggestion may be 
considered, if the reader chooses, as a mere simile ; but 
even so it may assist him in seeing the true relation 
between the idea which a name arouses, and the object 
to which that idea refers. The distinction between ob- 
jective reference and actual affirmation depends, as we have 
seen, on the difference between the analytic consideration 
of a connected group of judgments, and the affirmation of 
one among them. 

Extension 8. 1 now return to some further characteristics of the logical 

sion. n Cn meaning of names, and shall follow Mr. Bradley in using 
' idea ' for a fixed content or logical meaning, not for the 
psychical images which pass through the mind and never 
recur for the signification, so to speak, of the signal flags 
not for the particular flags themselves, whose meaning is not 
affected if different bits of cloth are used on every occasion. 

Insepar- i. Intension and Extension are complementary and insepa- 

rable, a. If an idea is the meaning or fixed logical content 

nature. indicated by a name, how does it come to pass that ideas 
or names are said to have two kinds of meaning, known as 
Intension and Extension ? The meaning proper, the fixed 
content, is obviously the Intension of the name or idea, 
sometimes inadequately defined as the meaning which the 
name implies, in contrast with the Extension considered as 
the whole range of individual objects or instances to which 

introd.j Intension and Extension, 47 

the name applies. But it is clear, as Mill has well insisted, 
that the intension is the primary meaning, or, as we have 
said, the meaning. To speak of it as implied or connoted, 
or as the connotation, seems therefore to be a terminology 
which Mill's own view should condemn. 

But if Intension is the meaning of a name, or is the idea 
which is this meaning, what is Extension ? How can a name 
mean anything beyond its meaning, or how can an idea, 
which is a meaning, yet have a further meaning? The 
answer is so familiar in practice that it seemed worth 
while to observe that it is not free from paradox. Ex- 
tension or Denotation consists of the instances, ideal or 
actual, in which any content is considered as realised or 
realisable. That is to say, extension is the aspect of 
a content as particular, or as an exclusive unit. The 
plural of a noun substantive affords the simplest illus- 
tration. ' Men ' form the extension or denotation corre- 
sponding to the content intension or comprehension of 
the name or concept ' man.' But ' a man,' the singular 
meaning correlative to 'men,' is extensive, just as is the 
plural itself. 

If there are two or more instances of the one content, 
the distinction between these particulars and the content 
itself is obvious ; if there is only one instance, and still more 
if there can be only one 1 , the relation is obscured. But 
in every idea the distinction between universal meaning 
and particular embodiment or exclusive self-identity can 
be traced, and neither aspect can be lacking in any idea. 
A name or conception without Intension would be a name 
without meaning, and therefore, also, without Extension ; 
for it is only the meaning that prescribes the Extension. 
And a name or conception that should have no Extension 
would be one that would not apply to any particular thing 

1 Sigwart, vol. i. p. 304, gives as an instance ' The centre of the material 
universe.' There cannot be two points, of which this content is true, but the 
meaning is still distinguishable from the particular instance, and is theoretically 
capable of having further particulars subsumed under it. Of course there may 
be two such points in succession the centre may shift. 

4 8 




cal ex- 

Names of 

or case, and therefore could have no Intension ; for the 
attributes which are thought of as embodied in particular 
cases are what constitute Intension. 

/3. This latter conclusion might be objected to on the 
ground that names of fictitious ideas or vain imaginations, 
or again nonsensical or self-contradictory expressions, have 
a sort of meaning, or at least find a place in would-be 
significant speech, and yet apply to nothing, i.e. have no 
Extension. 'Nothing' in this objection must mean nothing 
actual, if the objection is to be true in fact ; but actual in 
any determinate sense is a limitation or factor in Intension, 
and if we introduce it into an imaginary conception we create 
a contradiction and bring the fictitious idea or name under 
the head of self-contradictory or nonsensical expressions or 
conceptions, of which we shall speak directly. But if we 
do not take nothing to mean nothing actual, then the 
objection is not true in fact, and imaginary ideas, the 
content of absolute fictions, have their extensions in the 
instances, particulars, or units, or in the aspect of unity 
which they naturally imply. Chimeras, four dimensional 
space, Gulliver's voyage to Lilliput, have all the same 
complementary aspects of meaning and particularity that 
are involved in man, horse, or triangle. 

y. On the other hand, a word for under this head we 
can no longer speak of an idea which is unintelligible 
whether as a mere unknown noise or as a contradiction in 
terms with no rhetorical significance, is of course not a 
name, and cannot enter into the discussion ; for it has, 
strictly speaking, neither intension nor extension, so cannot 
illustrate the existence of the one apart from the other. 
Only it must be observed that even as a name or sign for 
a certain noise 1 the combination of letters has still its dual 
aspect of universality as an identifiable sound, corresponding 
to Intension, and particularity as a momentary and unique 
utterance corresponding to Extension. 

8. Another case is that of abstract names of attributes, 

1 See Bradley's Principles of Logic, p. 157. 

in-tkod.] Names of Attributes. 49 

such as ' whiteness,' ' virtue.' It is quite clear that these 
abstractions are true of particular instances. The simplest 
rule is to adopt as extension the meaning of the plural of 
the noun ; thus virtue becomes a generic conception, and has 
its extension in the virtues, i. e. the kinds of virtue, couf age, 
temperance, etc., and its intension in the generic meaning 
' a habit of volition directed to distinctively human ends,' 
or whatever our definition of virtue may be. Whiteness is 
not obviously a generic term, but has unquestionably a 
possible plural either in the sense of kinds of whiteness * or 
in the sense of instances of whiteness. In Latin as in 
English it is somewhat of a rarity to use the plurals of 
very abstract abstractions ; but yet they are sometimes 
used ; and besides, the difference between singular and 
plural only illustrates and does not constitute the distinction 
between Intension and Extension. As in the line quoted 
from Shelley, the singular whose meaning is on all-fours 
with that of one case among those indicated by the plural 
is itself a particular, and accentuates the extensional aspect 
of the idea. I may add that it has been well pointed out 2 
that such abstractions are ' doubly adjectival,' for they not 
only apply to real cases or kinds of the abstraction, 
whites ' or ' whitenesses,' but they actually mean the 
abstraction of a concrete thing or subject that has the 
attribute. They imply not merely particular whites, but 
particular things that are white. 

The intension of the simple abstraction ' whiteness ' is hard 
or impossible to state in general terms, if we leave out of 
account the theory of light, which has not been available for 
this purpose till a comparatively late date in the history of 
logic. A parallel difficulty caused Plato to say, at least at one 
stage of his views, that he could frame no eifios of a smell, i.e. 
he could find no general determinate attributes by which to 
formulate its definition. Such difficulties are plainly matters 
of the state of knowledge. A content which is recognisable 

1 Cf. Shelley's line, ' White with the whiteness of what is dead.' 

2 Bradley, Principles of Logic, p. 156. 
VOL. I. E 

5<d Introduction, [Introd. 

and identifiable in different contexts always has a meaning 
and intension. We are about to turn to two extreme cases, 
that of proper names and that of number, which will illus- 
trate the lowest grade to which the intension of a significant 
name can be reduced. No attribute, however hard to 
define, can be so indifferent to intensional meaning as the 
significance of a strictly proper name and the denomination 
of a number. 
Proper e. Proper names have sometimes been pronounced non- 

Names, connotative, i. e. without intension ; because their meaning 
is not fixed and generalised. On the other hand, Jevons, 
rightly rejecting this view, which is absurd because as we 
have seen intension and extension are inseparable, goes 
into the other extreme by refusing to distinguish Proper 
from Singular names, and therefore ascribing to the former 
a maximum of intension. By a proper name I understand 
primarily a name that merely serves to distinguish a place 
or person, or, in exceptional cases, a thing. As a rule, a 
thing which is neither place nor person has not the indi- 
vidual interest independent of fixed content which is the 
root of the employment of proper names. We name a 
thing according to its species, its type or function, not with 
reference to its absolute particularity. Cases like that of 
a favourite animal, e.g. a horse, to which a proper name is 
usually given, or even a favourite thing, such as Henry 
Smith's hammer Samson in ' The Fair Maid of Perth,' are 
exceptions that prove the rule. We can see that in such 
cases as these a special interest has come to be attached 
to the particular individual independently of its specific 
nature. By a ' singular ' name as contrasted with a proper 
name I mean a name that indicates content as such, but 
content that is in its nature, or at any rate assuming it to 
be located in the actual world, unique. Such is the instance 
given above, ' The centre of the material universe ; ' or, 
again, 'The king of England in the year 1832.' There is 
a certain difficulty in finding instances of these names, 
unless as in the last case we limit them in time, or as in 

introd.j Proper and Singzclar Names. 5 1 

'The chief murderer of Caesar' confer uniqueness upon 
them by relation to a true proper name. When we come 
to speak of the singular judgment we shall see that there 
is a good reason for this difficulty. It is prima facie im- 
possible for any content into which time does not enter to 
stand as the subject of a singular judgment. The centre 
of gravity of the material universe may shift its place and 
thus become in one aspect plural, though in another it 
remains unique. No idea can guarantee its own uniqueness, 
which is only given by reference to a position in the actual 
sensuous series. Still there is a difference between the 
singular and the proper name ; which I proceed to state as 
shortly as I can. 

Every name has intension and extension. But the 
extension naturally follows the intension, and the intension 
attaches to the name, without reserve ; that is to say, the 
name as such has a meaning, and is applied to all objects 
of which this meaning is true. Now the term ' proper,' which 
means in this usage ' peculiar ' or ' individual,' is in contra- 
diction with the above-mentioned characteristic of significant 
names, and imposes upon them a function with which the 
nature of intension is essentially at variance, viz. the recog- 
nition of individuals as such, in their particularity, and 
without primary reference to their attributes. Intension 
thus becomes a means and not an end. A significant 
general name is used of many objects in the same sense; 
and a significant singular name is used of one object only, 
because there is or can be only one object to which its meaning 
applies ; but a proper name, though used of many objects, 
is used of each in a different sense. Its rudiment of general 
meaning is in such an implication as that John is the name 
of a man and not of a mountain or a steam-engine; or 
again, some one of the thousand different applications of a 
proper name may become typical, and so set up a general 
meaning, which however does not attach to the name in its 
remaining 999 applications, but only elevates it into a term 
of ordinary language in respect of one application. I refer 

E % 

5 2 Introduction. [introd. 

to such cases as ' a Daniel,' ' a Croesus,' ' a Solomon,' ' the 
Rupert of debate,' etc. 

But these are abnormal uses in which the proper name 
ceases to be proper. The particular Johns, on the other 
hand, to whom the name John is applied as a proper name, 
do not form one extension corresponding to a single 
intension of this name. Each of them forms by himself a 
separate extension corresponding to a separate and distinct 
intension of the name John. The men called John are not 
related to their name as 'men' to 'man' or as 'towns' to 
' town, 5 but as Salviati's glasswork and the Pentateuch to 
' Mosaic,' or as a human being, and a cairn in the Lake 
Country, to ' man.' The subject is not without historical 
interest, but to pursue it would take us too far from logic. 
No doubt it might be maintained that in early language 
Interisional and Extensional meaning must to a great extent 
have coalesced. Whatever sound was appropriated to a 
sensible incident would at first, very possibly, attach itself 
only to the concrete or confused perception as a whole, 
and it might be long before pointing out the occurrence 
could be in any way distinguished from saying in what it 
consisted. Thus it might be said that language must have 
begun with proper names for everything, and advanced to 
general names, and only then had to face the problems arising 
from the necessity of identifying individuals by help of 
symbols whose nature is to be general. The problem is 
now solved to a considerable extent by a peculiar conven- 
tion as to mode of writing and amount of signification to 
be expected. We know that to find a town in Ontario 
called by the name of London justifies no single inference 
as to points of identity between it and the metropolis of 
England. We must keep etymology out of the question. 
A word means what it is used to mean, not what it once 
meant. The derivation of proper names justifies no infer- 
ence at all as to their meaning. The Remington type- 
writers bear the stamp of Ilion. In the same way inten- 
sional meaning cannot justly be ascribed to Christian names 


Introd.] Decline of Significance in names. 5 3 

or surnames, at least in modern England. There is now 
no legal monopoly of such names (though there may be of 
trading designations), and if we are taken in by ascribing 
intension of birth and breeding to a particular name, it is 
our own fault. But probably this state of things is modern, 
and the existence of proper names of persons in the full 
sense would in that case be modern also. If legal or social 
rights depended on bearing a particular name, then such a 
name had as an element of true intension those general 
relations patriciate, legitimacy, civic birth in which the 
right to bear it and the incidents of bearing it were involved. 
' The art of giving names,' it has been said, ' is lost.' It is 
certain that the purpose of mere recognition, to which all 
attributes are in their nature indifferent and serve only as a 
means, tends to destroy the picturesqueness of nomen- 
clature by dissociating it from interest in a general and so 
significant intension. The close relation between mere 
extensional meaning and the use of number is nowhere 
more strikingly illustrated than in the custom of number- 
ing not only houses but streets, as in great American 
cities. In the proper name there is still the semblance or 
fiction of a general Intension the special name-word seems 
indicative of distinct meaning ; in the number even this 
fiction has disappeared, and nothing remains but the place 
of the particular in an aggregate of particulars, united solely 
by a common denomination. 

Thus the distinction between a proper name and a 
significant name (whether singular, as God, or general, as 
1 man ') is that in the use of a proper name signification is 
a means to identification ; in the use of a singular or general 
name signification is predicated for its own sake. ' But the 
identification of a person or thing is signification,' it will be 
said. This raises the question of the nature of personal or 
individual identity, which is not in place here ; it is enough 
to point out that mere identification is a very barren kind 
of signification, since there is hardly a single attribute of 
actual content as distinguished from mere external relations 

54 Introduction. [Introd. 

that is necessarily conveyed by it. Macaulay after his 
mind was gone was still Lord Macaulay and his father's 
son, but what else was he that he had been ? 
Names with f. If pure Extension were to be found anywhere, it would 
j""^[ rat " be found in a general name or idea determined by number, 
or of which number is predicated. 

An extensional whole is an aggregate of individuals 
sharing a common nature, but regarded as particulars, i. e. 
as each identical with itself and external to all the others. 
This is, as we shall see more fully from the analysis of 
Enumeration (Book I. ch. 4), the nature also of a numerical 
whole. The unit of number and the particular of extension 
are closely allied. Each of them consists in the identity 
with itself of a concrete thing or discernible particular in 
spite of differences which it includes. Proper names also 
depend on this self-identity, but have for their purpose to 
single it out and mark it apart from the whole universe 
besides. Number does not seek to single out one such 
identity par excellence^ but to formulate the relations which 
arise between such discrete identities as factors in a sum or 
aggregate. In the first place then, number, though an 
attribute and so an element of intension, yet by accentu- 
ating the embodiment of a content in units external to one 
another, demands an extensional rendering of the idea. 
And in so far as depth of meaning is indifferent when we are 
thinking of aggregate units and not of connected attributes, 
so far the intension of a concept may be reduced to the 
denomination of a numerical aggregate. But if this remnant 
of intension, which determines the range of the aggregate, 
is removed, the thought is destroyed in both its aspects. 

And further, in the second place, a numerical determina- 
tion, although itself an attribute, tends to contradict inten- 
sion proper, and so force the attribute of extension or 
particularity into importance. It is obvious that in every 
concept the intension dictates the extension. And the 
extension so dictated must as an aggregate of instances be 
theoretically at least capable of representation by a number, 

introd.] Number and Extension, 55 

or if not, it must be in conflict with any and every number. 
We may omit the consideration of parts of space and parts 
of time, which seem to constitute a series that theoretically 
defies enumeration ; but no actual content of our real world 
can be thus infinite, so far as we can understand. The 
human race itself must, as we are bound to suppose, have a 
limited career, and the limitation, however far beyond our 
knowledge, must be immanent in man's nature in its 
relation to his environment. Thus the intension even of 
man, colour, gold, or other ordinary general names, must 
ultimately and theoretically imply a finite numerical aggre- 
gate of instances 1 . 

This number, which in such cases as the above we can 
never know, could be of no possible interest to us, were it 
not that it affects the import of any other number by which 
any such concept may be determined. In other instances the 
knowledge, which in the above cases seems not worth serious 
thought, is actually ours, or treated as being ours. Such 
instances are the three persons of the Trinity, the three sides 
of a triangle, the ten decemviri, the 670 members of the 
House of Commons, the five regular solids, the ninety degrees 
of a right angle. It will be observed that these illustrations 
display the number in very different relations to the inten- 
sion. A member of the House of Commons is no less a 
member if some units are withdrawn from the legal number 
of 670, as, in consequence of death or resignation is often, 
perhaps always, the case. The number in which he is a 
unit does not directly affect his position, although no doubt, 
if an immense proportion of seats were to become vacant 
owing to some extraordinary catastrophe, the House would 
be unable for a time to act as a House of Commons. The 
same is the case with the decemviri or the two Roman con- 
suls, for the authority of one member of these boards was 

1 This is, in so far as the instances are true individuals in a known system. 
Mere ' observations ' on the other hand, successive presentations to sense, must 
always be taken as entering into an infinite series, for no power can tell how 
often they may recur, nor what constitutes a single one. Nor do they by mere 
repetition tend to generate a system. 

56 Introdtiction. [introd. 

independent of that of the others or other. But if we take 
the case of twelve English jurymen the matter is altered, 
for the number is essential, though only made so by specific 
enactment, and if * a juror is withdrawn ' the others ipso 
facto lose their powers of trying a case, i. e. cease to be in 
the full sense jurymen. 

And it is possible for the number to enter even more 
deeply into the essence. Two sides without a third cannot 
be two sides of a triangle ; and an angle of one degree is 
not, considered in itself, a degree in a right angle. The 
nature of space as an ideal whole does indeed introduce 
a difficulty here, for it may be said that a degree can only 
be understood with reference to the circle, and therefore 
involves the conception of a right angle ; and that in space> 
a figure is all that it involves. The objection draws atten- 
tion to a principle which holds good of all units without 
exception, viz. that every unit ultimately involves the whole 
in which it is a unit, but it does not alter the fact that we 
have no right angle unless we have ninety degrees, while we 
have a House of Commons (unless Parliament is dissolved) 
so long at least as it has enough members to form a 
quorum. In other words, the whole implied in the unit in 
the one case involves a precise numerical determination, 
and in the other case does not. And it will be observed 
that as instances tend to approach the former type, the 
number ceases to be truly extensional, becoming as we shall 
see (Book I. ch. 3) a result due to measurement rather than 
to mere enumeration. The content, that is to say, no 
longer falls chiefly within each unit of the enumeration, so as 
to make the number a mere sign of the repetition of embodi- 
ments of the content, but in some essential respects is gene- 
rated by a repetition of the parts and does not exist in each 
taken alone. Thus, as was said, the character of being a right 
angle is not present in every degree of angular measure- 
ment, nor is the character of being a commonwealth present 
in every individual person not, at any rate, in the same 
sense in which the character of being a man is present in 

introd.] Collective Names. 57 

every person. A name or idea which, while involving a 
number of identical parts, is not truly predicated of each 
such part singly, was called in the old logic a collective as 
contrasted with a general name. Army e. g. is a ' collec- 
tive ' name as regards the individual soldiers in it, but a 
general name as applied to the English, German, French 
and other armies. The distinction indicated by the term 
was not valuable, for it was not explained. But it is 
obvious that a ' collective ' name or concept like ' army ' is 
a halfway house between the mere common nature of units 
like men, horses, books and the like, in which the enumera- 
tion of the particulars repeats the intension in every item of 
the extension, and wholes like nation, Parliament, triangle, 
plant, in which the parts are bound together by other rela- 
tions than that of number, and therefore their number does 
not form the extension of the whole, so much as an inten- 
sional attribute of that whole. Thus the enumeration of 
Englishmen is not so much the extension of the English 
nation, as it is at the moment an attribute of the English 
nation to contain such a number of Englishmen. The 
question is whether the content falls within the unit, or only 
within the synthesis of units. 

But whether mere units in an aggregate or elements in a / 
numerically determinate whole, numerable parts must have 
a number, which must directly or circuitously depend on 
intension. And every numerical determination other than 
that which thus springs from intension has the effect of 
erecting a mere whole of enumeration which, as regards 
the intension of the general name, is arbitrary and irrele- 
vant. An exceptional instance will illustrate this. Any 
two sides of a triangle are together greater than the third 
side. Here the two sides are not a mere whole of enumera- 
tion, and are not irrelevant to the conception of the three sides 
of a triangle. What is here predicated of them is a result of 
analysis applied to the triangle with its three sides, and is 
a consequence of the three-sidedness of the triangle. The 
three sides might indeed be named as subject in the pro- 

58 Introduction. [introd. 

position. But if we say ' There were 10,000 men in Hyde 
Park last Sunday' we have constructed a whole of enumera- 
tion prima facie irrelevant to the concept man and having 
an extension that conflicts with the extension of that con- 
cept, and therefore with the intension that dictates that 
extension. In other words, we have depressed the term 
1 man ' into the denomination or designation of the unit 
employed in counting. The number may if we choose 
be stated as a predicate, and the limit ' in Hyde Park ' 
taken into the qualification of reality which forms the sub- 
ject ; all that concerns us here is to point out that we are 
speaking of an aggregate framed ad hoc by enumeration, 
i. e. by taking men one after the other in their particularity 
up to a limit which does not prima facie present itself as 
implied in their nature. We not merely count men as par- 
ticulars, we count particulars if we count the angles of a 
pentagon, but we divorce them from their natural inten- 
sion by excluding the greater portion of the extension which 
it indicates. It is true then that number, qua mere 
enumeration, is, like the proper name qua mere identifica- 
tion, in a large measure antagonistic to intensional meaning. 
Alleged in- ii. The two cases which have just been discussed are 
of Exten- enou gh to show that not every variation of intension involves 
sion to In- a corresponding variation of extension, or vice versa. The 
essence of proper names and of numbers is to mark the 
same extension or the same amount of extension as persistent 
through intensions partially at any rate varying. Never- 
theless, the demand for a formal rule of inter-dependence 
between these two obviously connected aspects of concept 
and of judgment was satisfied in traditional logic by the 
doctrine that intension varied inversely as extension. This 
idea was an early development of the Aristotelian definition 
by genus and species, from which it obviously followed that 
whereas the generic attributes were contained together with 
others in the definition of the species, the individuals 
belonging to the species must be contained together with 
others among those belonging to the genus. Aristotle 

ixtrod.] The inverse ratio. 59 

noticed this consequence of his own views, but the false 
accuracy of the traditional rule was a later development 
of the forms which he established, when their life was 
beginning to fail. Recent logicians have more or less com- 
pletely condemned the doctrine in question ; perhaps the 
latest well-known writer who ascribed to it first-rate import- 
ance was Professor Jevons. His account excludes one 
obvious objection, viz. that a multiplication of identical 
instances cannot affect intension, by a proviso that only 
logical change of extension could affect intension. But this 
makes the view a truism ; if logical change of extension 
means admission into extension of a new kind as opposed 
to a mere multiplication of instances, it is obviously equiva- 
lent to some change, of whatever kind it may be, in meaning 
as such or intension. But even so, even accepting this 
proviso, it remains doubtful whether the doctrine of the 
inverse relation is important in any sense in which it is 
true. I am inclined, however, to think that the recent 
logicians to whom I have alluded, e.g. Sigwart, Wundt, 
and Bradley, and also to a smaller extent Lotze, err by 
sheltering themselves under a point of form, and avoiding 
the question of import. It is true, no doubt, that you may 
have any arrangement of concepts ; but it is hard, in view 
of our gigantic natural classifications with their unrivalled 
grasp of reality, to place any other arrangement of concepts 
on a level in real import with that of genus and species. 

I will begin, however, by going briefly through the weak 
points of the supposed law that the Intension of a concept 
or name varies inversely as its Extension. 

a. The quasi-mathematical phrase ' inversely as ' is The mathe- 
wrong. It asserts a ratio, and a ratio is a numerical rela- Xrase is 
tion. But in the case before us, one side of the matters wrong. 
compared does not lend itself to enumeration at all. The 
parts of extension may be counted, as we have seen, but it 
is inept to count the parts of intension. For they are not 
external to each other, and they form a whole such as 
cannot be divided into units except by the most arbitrary 

60 Introduction. [Introd. 

dilaceration. And if it were so divided, all its parts would 
vary in value, and there would be no reason to expect that 
ten of them (i.e. ten attributes) should have twice the 
amount or value of five. We must constantly bear in 
mind, e. g. in estimating the false doctrine of analogical 
inference, that there is absolutely no sense in counting 

It may be added that if we disregard Jevons' proviso 
the idea of a proportion is upset at once. The multiplica- 
tion of actual instances can obviously go on without affect- 
ing intension, so long as we adhere to the ordinary formal 
idea of an instance. Whether in strict reality every 
instance, at least in the organic world, must not constitute 
an infinitesimal step in evolution and therefore be an in- 
finitesimal approach to a new kind, is a further question. 
If the fact were so, it would merely have the result for our 
present purpose that every increase of extension must be 
treated as the addition of a new kind, and therefore as ipso 
facto affecting intension. It may also be pointed out that 
the mere existence of proper names as above explained, 
and of descriptions in Mill's sense, i. e. definitions used as 
practical guides to application, and to that end substituting 
some single mark for the whole complex of attributes which 
forms the intension of a concept, is enough to destroy the 
idea that the range of a concept's application must be 
altered as its depth of import is varied. 
Concurrent j3. But putting aside the mere pedantic form of the 
of r inten S ru -^ e anc * ^ e multiplication of identical instances, and taking 
sion and an increase of extension to involve a modification of kind, 
the substance of the rule may still be impeached. An 
increase of extension may even be conjoined with an 
increase of intension, either by the inclusion in the exten- 
sion of new instances which present attributes, previously 
unnoticed, in a striking form, or by the discovery of conse- 
quences or implications of the meaning or intension which 
show that a class of cases, not thought of in that connection 
before, are essentially sharers in the intension so understood. 

t<*rruA , e A^a / , 

Wc fy ; * V/<*V/iV *k ml*&*** '* view 

tf n . ~ ^LhtA* ff *<*wc# i /**/ *f hich 

Q/X C^v r ( 

I the 



*e of 

: the 

7 ( J ~ tne 



of it 

t, i.e. 



k*** ii i . <u )urely 

f/A^ o/ <a.wo w >>/ P^olc, f JMd^tA ., //" h' the 
/I ent of 

il v wef rv <^ 

i*r ass the 

[Jje new 

X^Ay .*Uv*U/**nf , ^ <*hui*w ixAJtfiHi i then 

lity in 

iM J!b t0 |*U^ &-*.< ' 'v^ kutte* /*>* i. ailing 

Doaies ciose to wc v^aimo o^.x^w^ . ___ extension 

increased by the inclusion of all material elements belonging 

1 The case in which the addition of attributes modifies the old attributes is 
the most interesting and the most typical. A content in which the attributes 
are not known as reciprocally modifying each other does not belong to a high 
phase of being or of knowledge. If the new instances do not remove any hin- 
drance in the way of accepting the new attributes, but merely lead to our 
detection of a new attribute as if by chance, it is hardly a fair case of increasing 
intension, it being so purely our own fault that we were not as wise before. 

C ft iL'/ *-> ^ 









U r,. 


the 1 

an ir 
If th. 
the m 
and o? 
some s 
idea t' 

Concurrent /3. 
variations ^ 

sion and an inci ^ .cat 

the substance of the rule may still be impeached. An 
increase of extension may even be conjoined with an 
increase of intension, either by the inclusion in the exten- 
sion of new instances which present attributes, previously 
unnoticed, in a striking form, or by the discovery of conse- 
quences or implications of the meaning or intension which 
show that a class of cases, not thought of in that connection 
before, are essentially sharers in the intension so understood. 

introd.] Increase of Intension. 61 

Thus, if we consider Rent from the Ricardian point of view 
as the element of profit that depends upon monopoly, 
we bring under the conception many species of gain which 
were never thought of in that light before say, for 
instance, the usurious interest which may be demanded 
for money when concealment is necessary to the borrower 
and he consequently cannot apply to the open market. 

But it will be replied, and I have purposely courted the 
objection, 'You are not increasing the intension, or at any 
rate you are diminishing it as well as increasing it ; you 
have stripped off all such attributes as " paid for hire of 
land, houses," etc., and so of course you can increase the 
extension of your idea of rent.' This is in a sense true. If 
new instances are included under a given intension, either 
they must possess the whole of it, and in that case their 
inclusion as such does not make any amplification of it 
necessary, for as it stands it is at least not incorrect, i. e. 
they are not new kinds, but mere instances, or they must, 
as in the above illustration, bring with them a modification 
of it which science chooses to adopt, and then, from a purely 
external and formal point of view, they must ' diminish' the 
given intension ; i. e. they must leave out some element of 
it. But this only shows how impossible it is to discuss the 
matter on the basis of counting attributes. The new 
instances may bring with them determinations far more 
concrete, penetrating, and constitutive of the reality in 
hand, than those that had to be omitted. We should then 
rightly say that the extension and intension had been 
augmented together \ When the conception of falling 
bodies close to the earth's surface' had its extension 
increased by the inclusion of all material elements belonging 

1 The case in which the addition of attributes modifies the old attributes is 
the most interesting and the most typical. A content in which the attributes 
are not known as reciprocally modifying each other does not belong to a high 
phase of being or of knowledge. If the new instances do not remove any hin- 
drance in the way of accepting the new attributes, but merely lead to our 
detection of a new attribute as if by chance, it is hardly a fair case of increasing 
intension, it being so purely our own fault that we were not as wise before. 

62 Introduction. [introd. 

to the solar system, then no doubt some such restriction as ' at 
the earth's surface' was stripped off from the intension of 
falling bodies, but on the other hand a determinate con- 
creteness of detail the inverse-quadratic ratio of attraction 
was added to this intension that made it far more full of 
significance than before. If we count every attribute for 
one we may say that the amount of intension in this case 
remains unchanged, but this would be a ridiculous con- 
clusion. What is one attribute ? 

The complementary proposition to that which began this 
paragraph does not in its natural sense apply to knowledge. 
Knowledge does not decrease, but only increases ; for the 
operations of forgetfulness are arbitrary and do not follow 
the laws of knowledge. I cannot therefore undertake to 
show that a decrease of extension may involve or be in- 
volved in a decrease of intension ; except in the sense that 
a change of classification may leave a name or recognisable 
idea robbed of much of its import, and also deserted by 
many of its instances. Thus the word ' Ecclesia/ which 
originally meant the whole visible church or congregation of 
believers in any locality, now, in its derivative ' ecclesiastic,' 
is applied to a sort of civil servants who exist within that 
body, and thereby has lost as notably in range as in import. 

But of course the mere formal complementary proposi- 
tion, that the lesser Intension may be conjoined with the 
lesser Extension, is only the other reading of the instances 
which show that the greater Intension may be conjoined 
with the greater Extension. 
Subsump- y. The whole idea that judgment and reasoning naturally 
or exclusively depend upon subsumption, i. e. upon taking 
attributes as connected simply within and by the unity of 
individual subjects, has of late been rejected, and with good 
reason. And with this idea disappears any formal or 
universal necessity that may have been supposed to attend 
the arrangement of attributes as designations of succes- 
sively wider aggregates of individual subjects. It is 
important that we should dismiss the notion that the 


introd] Truth of the ' inverse ratio! 6 


higher degrees of knowledge are necessarily and in the 
nature of intelligence framed out of abstractions that omit 
whatever has interest and peculiarity in the real world. 
Nothing has been more fatal to the truth and vitality of 
ideas than this prejudice, which I do not admit to be a just 
representation of the principles of Plato and Aristotle, 
although certain salient features of their doctrine gave it 
an unfortunate advantage. If the present reaction against 
formal logic should end in establishing a more vital con- 
ception of universality than that which sets it down to mere 
abstraction, a fundamental reform will have been made in 
philosophical first principles. 

iii. Nevertheless, subsumption and abstraction play a Truth of 
part in knowledge. It is not quite certain that there is any ' ln . ve y se 
judgment or argument which is incapable of being exhibited 
in subsumptive form. It is certain that to abstract and to 
distinguish to know what belongs to one relation, and 
what, again, though conjoined with that relation, yet does 
not arise out of it, but out of some other condition or cause 
is the first duty of the scientific intelligence. In conse- 
quence of this activity, arrangements of individual objects 
under a series of abstractions, each applying to a wider 
aggregate than the last, meet us on every hand, and most 
obviously of all in family relationships as estimated among 
civilised nations. The question before us cannot be dis- 
missed until we have treated it from this more real point of 
view. Is the ' pyramidal ' arrangement of concepts, sub- 
ordinating the less to the more abstract, scientifically con- 
venient, or, what in an ultimate sense comes to the same 
thing, is it true ? In answer to this question I will mention 
three points of interest. 

a. Sigwart reminds us that every concept may be re- Alternative 
garded from different points of view, and classification or lassifica- 
abstraction may therefore have different lines open to it : 
e. g. do we class a square first with four-sided figures, and 
then, subject to that limitation, with equilateral figures, or 
vice versa ? It is obvious that we put the square in quite 

64 Introduction, [introd. 

different company according to the order in which we apply 
these points of view. The point is that in this and similar 
cases we seem to have bona fide alternatives. No serious 
attention would be needed by the mere fact that we can 
class a copy of ' Paradise Lost ' either as a black or as a 
rectangular object. But if genuine alternative classifications 
are possible, it is clear that we may have a hundred objects 
before us, and being forced to divide them into classes 
from each of ten unconnected points of view, may be left 
with ten different classifications for each object, and apart 
from some peculiar ground there will be no reason for 
subordinating each object decisively to one classification 
rather than to another. 

The first remark that such a suggestion invites is that the 
idea of alternatives only touches the subordination of every 
object to one class or series of classes, but does not touch 
the alleged necessity of successively emptier abstractions 
within any one point of view which may be selected (as 
some one must always be selected at least pro hac vice) and 
adhered to. And, secondly, the mere difficulty of alterna- 
tives is inherent in the nature of intelligence, meets us in 
the problem of giving names, and is overcome in some 
degree whenever we venture to affirm a fact. In its most 
genuine form it is met by the theory of the relation 
between different sciences, to each of which the same 
individual thing obviously presents a different aspect. 
Sigwart's suggestion * of an inference to Pantheism from the 
doctrine of essence combined with that of subordina- 
tion because only the essence of the highest abstrac- 
tions is in no relation accidental seems to me perfectly 
wild. We should by this time be well aware that all 
essence is relative, but that relativity does not exclude 
absoluteness. One set of attributes are a man's essence 
qua citizen, and another qua parent. I may add that his 
argument depends on assuming that any class may be 
regarded in its turn as genus and as species. But this is 

1 Logik, i. 308. 

introd.] Individuals and Abstractions. 65 

an obsolete conception belonging to purely formal logic. $ 
The successive abstractions of classification have distinct 
characters expressed by definite titles and not interchange- 
able. A genus is not a species of an Order, and a Class 
is not the genus of a Division. 

(3. A group of objections which carry on the idea dis- Higher in- 
cussed above of abstraction by modification as opposed to 
mere neglect or omission of attributes, appears to me to be 
more important. If we look at a real individual into which 
other individuals enter as constituent parts, are we prepared 
to say that the containing whole (e. g. the state as compared 
with the citizen) has the less meaning or intension of the 
two ? The old logic would retort here that the extension 
of ' state ' is made up of particular ' states,' not of persons, 
or that that of ' nation ' or ' army/ consists in the several 
nations and armies, not in individual men and soldiers ; or 
that the extension of God is in his particular existence (as 
we do not here admit a plural) not in elements within God's 
being. But this would only meet the objection at the cost of 
narrowing the idea of universality to that of mere abstrac- 
tion, in contrast with the sense synthesis of differences in 
which we have taken it throughout. Moreover, even the 
aggregate of men, nations, or animals which is indicated by 
an abstract universal name has in virtue of that universal 
a common nature which is a germ of concreteness. A 
crowd is not an army, but it has in it always the ele- 
ments of a mob. As we saw above, collective names mark 
a mere half-way house from aggregation to individuality 
and it is a purely arbitrary procedure when examining the 
nature of universals, to restrict our notice to such as have 
attained to no higher embodiment than an aggregate of 
particulars. But in fact our prejudices would cause us to 
neglect a concrete nature if any such were apparent within 
the aggregate. We should insist that the idea which should 
include the states or nations of the world must have less 
import than the idea of England or France, and should 
therefore look for this idea in the abstraction 'state' or 

VOL. I. F 

66 Introduction. [introd. 

'nation/ neglecting to consider whether, e.g. as the source 
of international law, the aggregate of nations has not in it 
something beyond the elements common to various peoples, 
or whether, if this is not so, the absence of such a central 
unity is not at least a defect which we might hope to see 

But even if we yield to tradition so far as to conceive of 
all universality as arising by way of abstraction, we have a 
further difficulty to meet. It has been well pointed out 
that even abstraction in the scientific sense is not mere 
omission of attributes from the idea of a kind l . If, in a 
generic conception, all attributes were omitted which are 
variously modified in the species under it, the conception 
would as a rule be stripped of its entire content. That it 
could ever have been thought possible to distinguish be- 
tween attributes which are the same in all species of a 
genus, and attributes which are different in the different 
species, must have been owing chiefly to superficiality in 
the analysis of attributes and a neglect of their real con- 
crete character. It is easy to say that animality is common 
to men and beasts, while rationality belongs to men only, 
and in place of it animals have either instinct or nothing, 
and that therefore animality is the intension of the class 
which includes beasts and men, while each of these sub- 
classes has a separate and additional intension. But in 
fact the animality of men is quite different from the 
animality of beasts, and is not an attribute common to 
both in the sense in which a tree-trunk is the common sup- 
port of two of its branches. While on the other hand the 
thorough modifications which distinguish the intelligence 
of man from that of animals do not suffice to dissociate 
them beyond identification ; and the class-conception which 
simply omits all reference to intelligence is an inadequate 
class-conception for men and animals. Therefore the notion 
or abstraction which is to include both men and animals 
must on the one hand provide for a variable animality; 

1 Lotze, Logik, sect. 23. 

introd.] Abstraction without omission. 67 

must be considered, that is, not in the light of a fixed mark, 
but as a scheme of modifiable relations ; and must, on the 
other hand, find room for some reference to intelligence, 
and not simply strike it out as a mark in which the kinds 
to be classified are not the same. Prima facie then the 
content of the superior class-conception is made up of the 
very same elements as those of the conception nearer to 
individual reality, only that it must represent each attribute 
schematically, by limits of variation, instead of embodying 
a fixed system of amounts or values. It is obvious, how- 
ever, that this principle can only apply to the few most 
concrete abstractions nearest to sensuous reality, in spite 
of the allowance to be made for cases in which the total 
absence of an attribute in some subordinate kind may be 
intelligibly set down as an extreme instance of its fluc- 
tuation, and therefore does not require all reference to such 
attribute to be omitted in the class-conception to which 
the defective species is subordinate \ Even when we come 
to Organism as including both plant and animal, we must 
sacrifice, it would seem, something of content. It is hard 
to say whether we could ever be justified, for instance, in 
including sentience in the general idea of organism, in order 
subsequently, according to the principle just mentioned, to 
deny it to ' Plant.' The more general abstractions of the 
type just mentioned become rather groups of laws or condi- 
tions by which individuals are controlled than characteristics 
of the individuals in themselves. But that all their charac- 
teristics, besides being characteristics, rest upon conditions 
no less universal and absolute than these laws, this must 
never be forgotten. The question of mere marks which do 
not enter into the main line of natural classification has been 
treated above in speaking of alternative classifications. 
The truth of these alternative modes of looking at reality 

1 It is a common thing to find within a genus of plants which are not 
ranked as apetalous the entry referring to some one or more species ' Petals o.' 
In such a case the other species usually reveal minuteness or tendency to abor- 
tion of the petals. See on this whole subject, Lotze, Logik, sect. 23ff. 

F % 









is bound up with the question of the relative truth of the 
various sciences. 

Thus it is clear that immense deductions must be made 
from the traditional doctrine that Intension and Extension 
vary inversely. It has been seen that the one may vary 
without the other, that they may vary together, that infer- 
ence and judgment are not restricted to a subsumptive 
scheme, that individuals may be universal in a sense which 
does not depend upon abstraction, that thus the whole 
vraisemblance of the doctrine vanishes so far as the con- 
struction of individuals is concerned ; and that even if we 
deal with the abstractions of common classification the true 
proximate genus, as distinct from a mere abstract mark, 
has a content as rich as that of the species, though more 

y. "Nevertheless, I cannot think that Wundt is right in 
tracing the relations between class-idea and individuals to 
the mere effort of language to economise its store of words. 
The whole fabric of the organic and even of the inorganic 
world creates prima facie an overpowering impression that 
natural classification can correspond to reality. The per- 
ceptible fact of graduated affinity has in all ages taken 
precedence of its causal explanation. The facts of human 
or animal descent, so far as immediately observed and as 
embodied in systems of relationship, supplied a name, if 
not a thorough-going explanation, for the affinities observed 
in nature l . The degrees of family connection, at least in 
mature European society, are the simple prototype of the 
ordinary process of classification ; and the analogy has 
extended since the earliest days of Logic to the inorganic 
as well as to the organic world. Now the alleged relation of 
Intension and Extension may be simply illustrated by the 
characteristics shared by a group of first cousins, i. e. 
persons descended from the same grandparents, compared 
with those shared by second, third, or fourth cousins, whose 

1 See Lotze, Logik, sect. 30, on the probable original meaning of yevos 
and eUos. 


introd.] Truth of Successive Abstractions. 69 

common descent is more remote by one or by several 
generations. In the human race, indeed, individuality of 
mind and disposition has so much to feed it in special 
knowledge and experience that the phenomena are but 
irregularly observable ; but in the evolution of plants and 
animals their characters have the same graduated identity 
without the same deductions on the score of special training 
and mental development. And it is not only evolution 
by descent that will produce these pervading affinities. 
Cognate processes of causation result in kindred formations 
all through the world of inorganic substances; and even 
in the sphere of necessary ideas, of number and geometrical 
figure, identical relations, under varied conditions, produce 
the appearance of graduated kinship or affinity. 

Granting, therefore, in accordance with what has been 
said above, that the work of abstraction should be repre- 
sented not as selective omission but as constructive analysis, 
and that the blanks in a schedule of attributes common to 
a large range of existence are not mere blanks, but zero 
values that may become positive in some cases; still we 
cannot on the whole deny that the graduated operation of v/ 
natural causes is most fittingly embodied for knowledge in 
a hierarchy of abstractions. It is said that the summum 
genus, ' thinkable content,' or some such conception, must 
on such a scheme be empty and futile. But when we have 
surrendered the precise inverse ratio of Intension to Ex- 
tension, I see no ground for this reproach. Why should 
we pursue abstraction to a useless point to a point, that 
is, at which the conception which we reach ceases to be a 
penetrating and illuminating law? If philosophy has 
nothing sensible to say about thinkable contents as such, 
then we had better not pay attention to this highest ab- 
straction. But philosophy can hardly be expected to make 
so suicidal an admission. 

It must be remembered, however, that as has been shown 
above, where the higher concept is not a mere law, but a 
concrete real whole, the idea of diminishing Intension has 

jo Introduction. tintrod. 

no application whatever. It is for special knowledge to 
determine how far these different points of view are re- 
spectively to be taken. Psychology -subordinates the 
human soul to a set of laws which include, as they grow 
more abstract, a larger range of animal and organic exist- 
ence. Political science treats the same spiritual being in 
its concrete relations within an actual community of such 
beings not as a mere member of a class. To which of 
these two sciences that of Ethics ought to assimilate its 
procedure is a vexed question which illustrates the problem 
of deciding in what regions the rule of diminishing Inten- 
sion applies. 

One more suggestion may be ventured which aims, it 
will be said, at rehabilitating an old fallacy. I am unable, 
however, to persuade myself that it does not appeal to an 
unquestionable truth. I assumed above, for the sake of 
simplicity, that regressive abstractions such as figure in 
classification could represent in respect of their abstractness 
no character of reality. The grandparents from whom a 
cousinhood is descended have often a more real, marked, 
and individual character than their grandchildren, though 
what these latter retain of that character can only be repre- 
sented by an abstraction, much of it having been lost and 
supplemented from other sources. The grandparents are 
represented by an abstraction, in the existing first cousin- 
hood, but were not themselves in any way more abstract 
than their descendants. But when we look at long intervals 
of evolution the matter undergoes a change, as is easily 
verifiable in the case of human character and intellect. A 
savage has not the individuality of a modern European ; 
he is more abstract ; his nature includes fewer differences, 
less profound feelings, less grasp of fact, and less definiteness 
of imagination. Or to take a more tangible instance (for 
the facts of savage life are always subject to dispute if not 
to doubt), even the Greek intellect in its prime, or Greek 
art at its best, has not the many-sided concreteness that 
belongs to Shakespeare or Goethe, Raphael or Turner. 

introd.] From Abstract to Concrete. 71 

And indeed, if we go to natural history, and say that 
1 Organism in the abstract ' never existed, really the Amoeba 
or the white blood corpuscle seem to contradict us. It is 
hard to see how every successive generation or epoch of 
evolution, so long as growth is not counterbalanced by 
decay, can avoid adding import and significance to the 
content of things. With the mind this is admittedly the 
case, and the course of evolution seems to show it in nature 
too. It may be said that the antecedent is no more abstract 
than the consequent, and that the universe as a whole 
cannot grow either more or less concrete. But it may be 
doubted whether this formal argument applies to a system 
which has individuals within it. In bringing to bear its 
total content upon such individuals there seems to be 
scope for infinite grades of concreteness. In this case the 
advance from abstractness to concrete individuality would 
have grounds in historical fact. In one form or another 
this idea has often been maintained, and I think that it 
bears witness to a truth. 

We have now considered the primary aspects of the 
materials or instruments of logical thought the idea and 
the name. This discussion seemed appropriate to an 
Introduction, because it is impossible to admit that the 
name, concept, or idea, is a portion of the content of Logic, 
in the sense in which such a position is assigned to the 
Judgment and to Inference. We do not enter upon logical 
development proper till we come to deal with the evolution 
and affiliation of judgments. 


Of Judgment. 

I. The 

Nature of 
as such. 

Of Judgment and Judgment-forms in general. 

Judgment is co-extensive with affirmation and denial, 
or, which is the same thing, with truth and falsehood. True 
and false are not indeed terms applied exclusively to judg- 
ments ; but yet in all their applications their essential 
meaning depends upon judgment. The sensations of a dis- 
eased organ may be abnormal, but cannot possibly be false 
unless, on the strength of them, we judge erroneously. A 
false note is a real sound, a false man is an actual individual. 
It is not their existence, but a judgment implied in their 
nature, that gives meaning to the censure of falseness. The 
musical note is not what its place demands ; the man is not 
what he pretends or aspires to be ; it is the demand or pre- 
tension, ascribed actually or by metaphor to thing or person, 
which condemns them as false in as far as it is unrealised. 

Thus truth and falsehood are co-extensive with judgment, 
and depend on the fact which is its primary condition ; 
the fact that a thing may have an ideal relation to reality 
over and above its own particular existence ; so that its 
existence, though in itself real and actual, is empty and 
valueless in the absence of the further reality that such a 
relation demands. Truth must belong to something whose 
unreality is not simply non-existence ; or how could false- 
hood exist? The essence of falsehood or fiction is that 
there should be an actual something that pretends to be 
something else. 

Symbolic Ideas. y$ 

Thus if we describe Judgment as the act of thought which 
is capable of truth and falsehood, the description, although 
tautologous, is not unsuggestive. It tells us that we are to 
look for the differentia of judgment not in a mere mental 
fact, but in some further value with which the mere mental 
fact is invested. 

i. This primary condition of judgment recalls us to the Symbolic 
subject of the Introduction. In judging, we use ideas, ldeas " 
but the ideas which we use are not mere particular 
mental images, the perishing existences which pass through 
consciousness, and which, qua particular psychical states 
on a level with mere sensations, never recur. Ideas 1 , 
according to Locke, though particular in their existence, 
are general in their signification. In judgment, ideas 
are employed solely for the sake of their general signifi- 
cation, and without reference to their particular existence. 
An idea, considered as a general signification, is what was 
described in the Introduction as the meaning of a word. It 
is not without effort, as we all know, that we can find in our 
consciousness any intermediary between the word on the 
one hand, and the reality on the other; and when it is 
brought to our notice that a reality cannot as such be a 
state of our individual consciousness, we are sometimes 
tempted to deny that it has any representative there 
beyond the name. We see from this how utterly the sym- 
bolic and secondary employment of psychical images 
obliterates all consideration of their particular existence as 
mental occurrences. We no more take note of them than, 
on meeting a welcome friend, we give ourselves a detailed 
account of the peculiarities by which we recognise him. 
The word and its reference a reference to some continued 
identity in the world of meanings 2 are inextricably welded 
together. It is only by reflective analysis that we discover, 
within and auxiliary to the meaning of a word, the par- 
ticular psychical images by help of which we symbolise it. 

1 Essay on Human Understanding, Book III. chap. 3. sect. 11. 

2 See Introduction, sect. 7. 

74 Judgment and Judgment-forms. [book i. 

And the meaning tyrannises over the psychical image in 
another respect. Besides crushing out of sight its particular 
and exclusive existence, it also crushes out part of its con- 
tent. The psychical images that pass through our minds 
might be compared to a store of signal flags. Not only is 
it indifferent whether your signal flag of to-day is the same 
bit of cloth that you hoisted yesterday, but also, no one 
knows or cares whether it is clean or dirty, thick or thin, 
frayed or smooth, so long as it is distinctly legible as an 
element of the signal-code. Part of its content, of its 
attributes and relations, is a fixed index which carries 
a distinct reference; all the rest is nothing to us, and, 
except in a moment of idle curiosity, we are unaware that 
it exists. The well-known difficulty of detecting misprints 
arises from the same despotism of the meaning. Let the 
main index-letters of a word be correct, or even the main 
index-words of a sentence, and we are off at once in thought 
to the word or sentence which is indicated, and remain 
unaware of minor variations in the content employed as 

Thus the idea, as used in judgment, is a general sig- 
nification, or in other words, a fixed reference. And 
because fixed, it is limited ; limited to portions of content 
which serve as indices of the reference, and are compatible 
with psychical accompaniments that vary with the series of 
mages. I will give another instance. Some one speaks 
to me of the Aegean Sea, which I have never seen. He 
tells me that it is a deep-blue sea under a cloudless sky, 
studded with rocky islands. The meanings of these words 
are a problem set to my thought. I have to meet him in 
the world of objective references, which as intelligent beings 
we have in common. How I do this is my own affair, and 
the precise images at my command will vary from day to 
day, and from minute to minute. It sounds simple to say 
that I combine my recollections of sea and sky at Torbay 
with those of the island-studded waters of Orkney or the 
Hebrides. Even so, there is much to adjust and to neglect ; 

chap, i.] Non-Symbolic Ideas, 75 

the red cliffs of Torbay, and the cloudy skies of the north. 
But then again, my recollections are already themselves 
symbolic ideas ; the reference to Torbay or the Hebrides 
is itself a problem set to thought, and puts me upon the 
selection of index-elements in fugitive images that are 
never twice the same. I have first to symbolise the colour 
of Torbay, using for the purpose any blue that I can call 
to mind, and fixing, correcting, subtracting from, the colour 
so re-called, till I reduce it to a mere index-quality ; and 
then I have to deal in the same way with the meaning or sig- 
nificant idea so obtained, clipping and adjusting the qualities 
of Torbay till it seems to serve as a symbol of the Aegean. 

Here then we have the first essential of judgment. The 
ideas used in judging are not particular existences but 
general significations, or objective references. No mere 
mental occurrences as such, no series or combination of 
particular images, can by any possibility be a judgment. 
It is the essence of judgment to claim a value which is 
beyond the mere mental act itself, and which is therefore 
liable to be divorced from the mental act ; and this divorce, 
as we have seen, is what falsehood means. That is false, 
which is, but like a false coin, has not the significance which 
it claims. In judgment, then, all ideas are symbolic, that 
is to say, have a constant reference. 

Can ideas be symbolic apart from judgment? If no 
ideas in a human consciousness are apart from judgment 
(see Introd. 2. ii) this question falls to the ground so far as 
concerns that consciousness. But the discussion referred 
to made it clear that apart from ultimate analysis we do 
entertain ideas without judging them true, as in the question 
and in the negation, and that these ideas are symbolic. The 
further problem may then be pressed upon us : ' Are there 
at all ideas which are not symbolic ? ' In identifying the 
human intelligence with a continuous judgment we seem to 
have denied in advance that non-symbolic ideas are, for that 
consciousness. The answer is that a. In judgment itself the 
idea can be distinguished qua particular in time or psychical 

7 6 

Judgment and Judgment-forms. [booki. 

to reality. 

fact, and so far is not symbolic, and /3. In all those human 
experiences from which we draw our conjectures as to the 
animal intelligence, when in languor or in ignorance image 
succeeds image without conscious judgment, we feel what it 
is to have ideas as facts and not as symbols. 

ii. Granting that symbolic ideas cannot ultimately be 
entertained without judging, it does not follow that to judge 
is merely to entertain ideas. In what does the act of judg- 
ment consist ? An act it undoubtedly is ; an act which is 
as certainly present, and which we find as hard to describe, 
as the much disputed act of volition itself. 

I shall attempt in the first instance to make the essentials 
of the matter quite clear in a simple case, with which we 
shall afterwards find that all more elaborate instances agree 
in fundamental structure. 

If I say, pointing to a particular house, 'That is my 
home,' it is clear that in this act of judgment the reference 
conveyed by the demonstrative is indispensable. The 
significant idea, ' my home,' is affirmed, not of any other 
general significant idea in my mind, but of something 
which is rendered unique by being present to me in per- 
ception. In making the judgment, 'That is my home,' 
I extend the present sense-perception of a house in a 
certain landscape by attaching to it the ideal content or 
meaning of 'home' ; and moreover, in doing this, I pronounce 
the ideal content to be, so to speak, of one and the same 
tissue with what I have before me in my actual perception. 
That is to say, I affirm the meaning of the idea, or the idea 
considered as a meaning, to be a real quality of that which 
I perceive in my perception. 

The same account holds good of every perceptive judg- 
ment ; when I see a white substance on a plate and judge 
that ' it is bread,' I affirm the reference or general meaning 
which constitutes the symbolic idea ' bread ' in my mind, to 
be a real quality of the spot or point in present perception 
which I attempt to designate by the demonstrative ' this.' 
The. act defines the given but indefinite real by affirmation 

chap, i.] The Constructed Real World. 77 

of a quality, and affirms reality of the definite quality by 
attaching it to the previously undefined real. Reality is 
given for me in present sensuous perception, and in the 
immediate feeling of my own sentient existence that goes 
with it. The real world, as a definite organised system, 
is for me an extension of this present sensation and self 
feeling by means of judgment, and it is the essence of 
judgment to effect and sustain such an extension. It 
makes no essential difference whether the ideas whose 
content is pronounced to be an attribute of reality appear 
to fall within what is given in perception, or not. We 
shall find hereafter that it is vain to attempt to lay 
down boundaries between the given and its extension. 
The moment we try to do this we are on the wrong track. 
The given and its extension differ not absolutely but 
relatively; they are continuous with each other, and the 
metaphor by which we speak of an extension conceals 
from us that the so-called ' given ' is no less artificial than 
that by which it is extended. It is the character and 
quality of being directly in contact with sense-perception, 
not any fixed datum of content, that forms the constantly 
shifting centre of the individual's real world, and spreads 
from that centre over every extension which the system of 
reality receives from judgment. 

Waiving then this distinction, though as a matter of 
degree it may find a place in the enumeration of judgments, 
we find the same general features in all judgments of 
perception. There is a presence of a something in contact 
with our sensitive self, which, as being so in contact, has 
the character of reality ; and there is the qualification of 
this reality by the reference to it of some meaning such as 
can be symbolised by a name. It cannot be alleged in 
theory that a name is essential to judgment. At least for 
'name' it would be necessary to substitute in such an 
allegation 'some symbol.' The spatial order of things 
which we see whenever we open our eyes, is, qua order 
of things, the content of a perceptive judgment, in 

78 Judgment and Judgrnent-forrns. [book i. 

which universal ideas are presented through sensuous 

The subject in every judgment of Perception is some 
given spot or point in sensuous contact with the percipient 
self. But, as all reality is continuous, the subject is not 
merely this given spot or point 1 . It is impossible to 
confine the real world within this or that presentation. 
Every definition or qualification of a point in present , 
perception is affirmed of the real world which is continuous 
with present perception. The ultimate 2 subject of the 
perceptive judgment is the real world as a whole, and it 
is of this that, in judging, we affirm the qualities or 

The claim to be true, which as we saw belongs primarily 
to judgment, indicates the same relation. In every judg- 
ment, as Mill incisively contends, we profess to speak 
about the real world and real things. ' The Sun ' means 
' the Sun ' ; and whatever that may be, it is not anything 
merely in my mind ; not relative purely to me as a conscious 
organism ; not a psychical fact in my individual history. 
Every judgment, perceptive or universal, might without 
altering its meaning be introduced by some such phrase as y 

' Reality is such that ,' ' The real world is characterised 

by .' 

Thus in the Perceptive Judgment at least we find the 
meaning or objective reference of an idea such a content 
as is indicated by a name affirmed to characterise some 
reality present in sense-perception, and through it, reality 
as a whole. We shall find that all Judgments of every kind 
share the main elements of this description ; only that the 
reference to an indeterminate element of present sense- 
perception is gradually displaced by the introduction of 
explicit ideas to designate the immediate subject. Such 

1 See Introd. 2. i. 

2 See Introd. 2. i. Analysis and cross-examination readily verify this as a 
fact. After admitting any judgment to be true, you cannot deny its modifying 
effect on any portion whatever of your real world ; i. e. it has been admitted of 
the real world as a whole. 

chap, i.] The Proposition. 79 

ideas disguise but do not remove the reference to Reality as 
the ultimate subject in every judgment ; they have, however, 
important effects in modifying both the act of affirmation, 
and the nature of what is affirmed. When I come to 
examine the chief types of judgment, I shall have to 
consider the nature of these effects. But I intend in the 
first place to say something of the proposition, from the 
analysis of which many current views about judgment are 

iii. The enunciative sentence the unit of language judgment 
which represents a judgment is called a proposition. a f n rop ~ 
Language, as we saw, supplies the fixed symbols which 
stand for ideas. It would be rash to say that there can be 
thought without language if language includes every pos- 
sible system of recognisable signs and wholly perverse to 
imagine that the ideal of intelligence lies at all in the direc- 
tion of a severance of thought from words. The Introduc- 
tion, in dealing with Names, showed us the absurdity of 
any such conception. But yet the spoken or written pro- 
position differs fundamentally from the judgment. 

I do not think that it is convenient to rank the narrative 
or temporal affirmation as a 'proposition' (German "Satz'), 
and reserve the name of judgment for an act of thought 
which has some purpose in the way of classification or 
definition. To do so is in English terminology at least to 
confuse a distinction of degree with one of kind ; but it is 
worth noticing that such a nomenclature has been pro- 
posed \ and that according to it judgment proper would 
begin at the point where inference and necessity become 
explicit. For against any doubt, judgment maintains itself 
as an inference 2 , and this is exactly the test that has been 
held to distinguish a judgment from a proposition. To 
affirm that a carriage is passing the house, Hegel says 1 , is 
not a judgment unless there is a question, e.g. whether it 
is a carriage or a cart ; i. e., I suppose, unless some general 

1 Hegel's Logic, Wallace's Translation, pp. 258-9. 

2 Bradley, Principles of Logic, p. 404. 

80 Judgment and Judgment-forms. [Book i. 

connection of attributes is intentionally affirmed. Now a 
general connection involves a ground, and so an inference. 
Thus the classification in question would have the merit of 
suggesting that judgment begins with inference. But the 
point of commencement taken is really arbitrary ; though 
judgment and inference begin together, yet both begin 
before this point. 

I prefer then to take the proposition all through as the 
actual spoken or written enunciative sentence; while the 
judgment is the intellectual act which depends in various 
degrees upon words or other symbols, but is different from 
any mere combination of words or symbols whether heard, 
read, or remembered. 

The essential differences between judgment and proposi- 
tion may be arranged under two heads, which cannot how- 
ever be wholly separated from each other. I shall first 
speak of the so-called parts of the judgment, the current 
conceptions of which are derived from grammatical analysis 
of the proposition ; and then pass on to consider how far 
the idea of a transition in time, which is inseparable from 
the apprehension of a sentence, is applicable to the judgment 
as such. 
The a. The division of the Judgment into Subject Copula 

ratiHneaL anc * P recu cate is obviously derived from the analysis of 
the enunciative sentence. The finite verb, which is 
a proposition in miniature, contains all these elements 
within itself; and the history of their being distin- 
guished within the sentence is the history partly of lin- 
guistic evolution and partly of grammatical or quasi-logical 
analysis. Even the separation of the substantive from or 
within the verb, is, I suppose, an early analytic develop- 
ment of language ; and it is the tendency of modern 
speech, no less than a supposed convenience of thought, 
that has finally transmuted Nominative and Verb into 
Subject Copula and Predicate. The Copula in the modern 
sense was unknown to Aristotle, although the use of the 
predicative Verb 'to be ' attracted his attention and drew 

chap, i.] What pai'ts has the Judgment? 81 

from him a somewhat inadequate explanation. If we 
return, however, to Aristotle's main position, and, in agree- 
ment with students of English grammar 1 , regard the Judg- 
ment as made up of Subject and Predication (oro^a and 
prjjuuz), we have got rid of one fiction in the separate Copula, 
but the distinction which we retain may still be challenged. 
It is plain that the judgment, however complex, is a single 
idea. The relations within it are not relations between 
ideas, but are themselves a part of the idea which is predi- 
cated. In other words, the subject must be outside the 

judgment in order that the content of the judgment may k 

be predicated of it. If not, we fall back into ' my idea of 
the earth goes round my idea of the sun/ and this, as we 
have seen, is never the meaning of 'The earth goes round the 
sun.' What we want is ' The real world has in it as a fact 
what I mean by earth-going-round-sun.' 

This view, stated thus extremely, would not only annihi- 
late the copula with separate content, but also the whole 
distinction of Subject and Predication, and it is an argument 
in its favour, that, in doing so, it would seem only to lay 
bare in all judgments the elementary type which forces itself 
on our observation in the simplest perceptive apprehension ; 
at a stage, that is to say, before the grammatical subject, 
which creates our present difficulty, appears explicitly in the 
proposition. But we shall see in tracing the evolution of 
judgment, that it is impossible to dispense with the distinc- 
tion of Subject and Predication, and that the appearance of 
contrast between propositions which have and which have 
not grammatical subjects, is caused by the necessity of 
representing immature thought in developed language; so 
that the thought in which distinctions are rudimentary 
must either be mutilated by the omission of an element, or 
transformed by explicit articulation. It is impossible to 
represent a judgment by a single noun belonging to a 
modern language, though such a noun is often all that we 

1 Cp, Mason's English Grammar, Jones's Analysis of English Sentences, and 
Wrightson's Functional Elements of the Sentence. 
VOL. I. G 


82 Judgment and Judgment-forms. [booki. 

utter. Such a judgment should really be represented 
either by a rudimentary sentence, that is, by some element 
of language not yet reduced to the position of a part of 
speech, or by a miniature sentence, i.e. by a verb. 

In other words, although the ultimate Subject extends 
beyond the content of the judgment, yet in every judgment / 
there is a starting-point or point of contact with the ulti- 
mate subject ; and the starting-point or point of contact 
with reality is present in a rudimentary form in the simplest 
perceptive judgment, as it is explicitly in the later and 
more elaborate types. 

Then it would come to this. Subject and Predicate in 
the actual judgment are really distinct, as a real identity 
from or in its differences. The relation of their contents 
is itself ideal, and not a relation between ideas ; but never- 
theless the judgment demands this relation ; for the judg- 
ment is my consciousness qua judging^ and my conscious- 
ness in judging identifies the ideal or symbolised reference 
which constitutes the predication with its own construction 
of the Real world \ 

The difficulty is that you cannot affirm without intro- 
ducing a distinction or reference into the content of the 
affirmation ; and yet such distinction or reference, being 
part of what is affirmed, and not a relation between what is 
affirmed and something else, cannot, it would seem, be the 
essence of the affirmation. What is the connection be- 
tween the two things; between the reference of 'is-building- 
a-wall ' to ' Balbus,' and the affirmation that the whole idea 
' Balbus-building-a-wall ' is true of reality ? What has the 
action of Balbus to do with my affirmation that Balbus 
acts? The latter seems wholly unconnected with the 
former, and yet they are inseparable. 

And the answer is that the real world is primarily and 
emphatically my world. I take it to be real in virtue of its 
contact with me. Therefore though the ideal relation 
within a judgment is not a psychical fact in my mind but a 

1 Cp. Introd. 2. i. 

chap, l] Subject, in Logic and Grammar. 83 

fact affirmed objectively of the real world, yet, the real world 
for me being the world that hangs from my present per- 
ception, I identify my assertion about it with its assertion 
of itself. In every judgment the ultimate subject Reality 
is represented by a selective perception, or idea, which 
designates a something accepted as real. This something, 
taken as standing for reality, is the actual subject of the 
judgment, and is qualified by the ideal content which forms 
the predication. No judgment can be found in which Sub- 
ject and Predicate are not apparent. Reality is one, but its 
presentation varies ; and it is impossible to judge without 
explaining where and how Reality accepts the qualification 
which we attach to it. The presentation of Reality, quali- 
fied by an ideal content, is one aspect of Subject and 
Predication ; and my individual percipient consciousness 
determining itself by a symbolic idea, is the other. That 
the latter is identified with the former follows from the 
claim of conscious thought that its nature is to know. 

Thus I am of opinion that Subject and Predication are 
essential elements in the Judgment. But whereas in the 
judgment they are differences within an identity, in the 
proposition they are isolated parts of an extended whole ; 
and the copula, which in Judgment is merely the reference 
that marks predication, and has no separate content, be- 
comes in the proposition an isolated part of speech. When 
therefore the analysis of the proposition controls the inter- 
pretation of the judgment, each of these parts of the 
sentence is treated as a separable content, and perhaps as a 
separate psychical existence ; and we are told of two ideas 
or two ideal contents, and a variable copula, itself also an 
ideal content, which indicates the varying relations l between 
them. In this sense Subject and Copula and Predicate 
are mere fictions. The judgment is not a relation between 
ideas, nor a transition from one idea to another, nor does it 

1 Lotze, Logik, sect. 52. It is very doubtful whether in this passage Lotze 
escapes the error which he imputes to others, of reducing a logical operation 
to a mere psychical occurrence.' 

84 Judgment and Judgment-forms. [booki. 

contain a third idea which indicates a particular kind of 
connection between two other ideal contents. 

The real nature of the copula we have seen already. It 
is the mere sign of affirmation, and, though usually con- 
veyed by a finite verb in languages which possess one, does 
not depend on tense. Aristotle, who was inclined to in- 
clude ' indication of time ' in the differentia of affirmation, 
was nevertheless aware that judgment could take place 
'absolutely' (a7rA.<3s) as well as with note of time (Kara 
Xpovov). Moreover a verb can exist without definite tense, 
and predication can exist apart from a distinctly formed 

The reason why the verb, where there is a verb, is appro- 
priated to the act of predication, is not that the verb signi- 
fies time, change or action, but that it is, as has constantly 
been repeated, a miniature sentence. Not merely does the 
verb 'agree' with its subject the adjective also agrees 
with its substantive but by convention, or explicitly in 
the person-ending, it includes within itself a reference to 
given reality, and can therefore stand alone as an enuncia- 
tion, which no other part of speech can do. In other 
words, the verb is prima facie a content referred to a real 
individual subject, and though the subject may be by the 
help of additional phrases defined, set down as imaginary, 
or even denied, the verb has always in itself the force of 
this demonstrative reference. An adjective implies a re- 
ference to something else, but the something may be a 
mere idea ; it is only the verb that professes to select an 
element directly related to the speaker's apprehension, and 
to attach a significant content to that element. 

It is in the demonstrative force of the verb that we must 
look for its fundamental predicative force. I suppose that 
the collocations which in Greek, and more or less in many 
languages, have power to turn the epithet into a predicate, 
owe their significance to a quasi-demonstrative emphasis. 
In ' the white horse ' (6 Xcvkos Xttttos) there is nothing that 
can be taken as a reference to a special point in reality; no 

chap, i.] Is Judgment a change hi time? 85 

indication of a real existence, either in the ideal content or 
out of it, which we propose to qualify by its meaning. In 
1 the horse (is) white' (6 twos XevKos) there is an indication 
of a line between a an individual that may be real and j3 
a content that may be attached to him or it, and therefore 
the instinct of reason which sees a judgment wherever a 
judgment is possible, takes the individual named as if it 
were an appeal to perception, i. e. a demonstrative reference 
to reality, and the content as a quality ascribed to the 
real subject so obtained. In the universal judgment this 
demonstrative reference becomes merely formal ; but it con- 
tinues in all language to supply the symbol of judgment. 

/3. It has been proposed to distinguish Subject and Judgment 
Predicate simply as earlier and later in time, and the above [" xime n 
instances of demonstrative reference appear to support this 
notion. But rather than admit it to be correct, I should 
surrender the distinction altogether and adopt the view 
that there is no subject in the judgment as such. For it is 
absolutely impossible that priority in time should subsist 
between the parts of a completed judgment. But if not, 
the priority of the subject would exist merely in memory; 
and an act of thought cannot be characterised by a mere 
recollection of the process that generated it. 

In what sense is it true that the Judgment is in time, and 
in what sense not ? It may be convenient to distinguish 
between arriving at the judgment, and subsequently modi- 
fying the judgment, although the two processes are, as we 
shall see, really continuous. 

In what follows I do not identify the aspect of Judgment 
as in time with the series of images qua psychical occur- 
rences that pass through the mind while we judge. It is 
probable that the view which defines Judgment as a change 
is influenced by the particularity of ideas qua events of 
consciousness as well as by the constant transition from 
judgment to judgment. But the former element ought to 
have been eliminated by what has been said above. 

1. In arriving at a Judgment, as when we hear a sentence Arriving at 


86 Judgment and Judgment-forms. [booki. 

and ' wait for the verb/ or scrutinise an approaching person 
until his name comes into the mind, we undoubtedly appear 
to begin with a ready-made Subject, to which a Predicate is 
added by a subsequent transition. But closer attention will 
show us that this is not the case. We have always some 
anticipation of the meaning of a sentence, and this antici- 
pation takes the shape of a provisional judgment or judgment 
in outline, very probably disjunctive in type, the shape of 
which becomes more definite as we follow the sentence, 
until the final clause determines its ultimate content. In 
the first place, consciousness, when any ideal content what- 
ever is presented to it, absolutely refuses to abstain from 
judging ; and in the second place, what comes first could 
not have (as it undoubtedly has) the significance of a 
subject, unless with reference to something already referred 
to it ia the way of predication. 

The case of perception leads to the same conclusion. 
You can come to no judgment by help of perception 
unless you interrogate perception ; and you cannot interro- 
gate perception unless you have in the mind some general 
idea as a basis for further specification. 

Thus, in reaching a particular apprehension or perception, 
there is a transition that occupies time. But the transition 
is not from Subject to Predicate, which we will call 5 and P 
respectively, but from s-py (where y indicates superfluous 
detail, which is omitted when the perception becomes 
clear) through 2-IT, to S-P. To speak of a transition 
from vS to P is wholly false. We never have an 6" first, 
and then tack a P on to it ; we have always an inchoate 
judgment or a choice of judgments. The process is not 
like adding one piece in a mosaic to another ; it is more like 
enlarging a hole, which has centre and circumference from 
the beginning. 
The 2. What has been said of the transition by which we 

Judgment, arrive at a judgment cannot but apply to the judgment 
when arrived at. It is clear indeed that we are thus led to 
regard the completion of the judgment as an arbitrary 

chap, l] Judgment is extended in time. 8 7 

distinction, dependent solely upon our momentary interest. 
The completed judgment, like the process by which it is 
obtained, obviously possesses duration. It is absurd to 
suppose that a judgment cannot be dwelt upon, and only 
exists as a momentary transition from 5 to P. Such a 
conception arises from the confusion of two points of view, 
either of which may be taken as a presupposition, and 
reconciled with the other by a mistaken compromise. It 
may be assumed that the judgment, as such, is not in time, 
and then this assumption has to be reconciled with the 
obvious fact that judgment as an intellectual process is a 
transition that occupies duration ; or it may be taken as 
certain that the judgment is a transition in time, and then 
we have to face the experience that its essential parts do 
not fall outside each other in succession. To treat it as an 
instantaneous transition is a ridiculous attempt to combine 
the character of occupying duration with that of not being 
in succession. It recognises both principles, and satisfies 

As we have seen in the process of arriving at the judg- 
ment, the act of judging as an occurrence in consciousness 
presents itself in the aspect of an interval of consciousness 
extended in time, and therefore including successive 
differences within it. But it does not include succession 
because the nature of the judgment is to be successive, but 
because the flux of sensations and ideas is always pressing 
new material upon consciousness, and a perception, once 
attained, satisfies no interest by being further dwelt upon 
unless it gains in content from moment to moment. Thus 
the duration of the judgment as a transition in time is, so 
to speak, its external aspect, the aspect which, as a whole, 
it presents when compared with other occurrences in con- 
sciousness ; and this duration is theoretically capable of any 
degree of extension. On the other hand, as between Sub- 
ject and Predication, that is to say, within the judgment, 
there is no transition at all. 5 and P are modified pari 
passu, and so, as a relation between them, the judgment is 

88 Judgment and Judgment-forms. [booki. 

not in time. This relation is a continued identity S-P 
which includes within it the differences s-p, 2-17, and so 
on. The transition is not from 5 to P, but from s-p to 
2-n within the general signification S-P. The idea of 
mere momentary existence has therefore thus much truth, 
that if you cut across the interval of consciousness occupied 
by a single judgment at any point whatever, you will 
always find in the plane so laid bare both 5 and P in one 
or other of their forms. They are in every minute part, 
but they are not confined to such a minute part. Judgment 
breaks up into judgments as rhomboidal spar into rhom- 
boids, but nevertheless it is one through its whole ex- 

But if a judgment can be thus extended, what do we 
mean by a judgment, and how do we know when we enter 
upon & new one ? The question is in each case a material 
one, being in fact the question of continued identity, and it 
is impossible to give it a formal answer. As a first ap- 
proximation we might say that a single judgment is any 
extent of judging activity that can be summed up in a single 
proposition. But as the proposition takes its value from 
the judgment, and not vice versa, this is no more than an 
appeal to the fact that we succeed in distinguishing single 
judgments. The question is one of continued identity, and 
therefore must be dealt' with as concerning organised 
wholes or systems. A mere extension of a system, or a 
mere omission within a system, does not bring us to a new 
and different system. The clearest cases of transition from 
judgment to judgment are those in which language uses a 
mere conjunction. When, on the other hand, we have 
propositions united by the inferential particle, it is a 
matter of degree how far they stand for separate j udgments. 
Ultimately perhaps every inference may or should be 
[y represented as a single judgment, as being a mere extension 
of an existing whole of thought, and not a transition to a 
different one. Such an idea conflicts with the traditional 
differentia of inference, that it should lead to a new judg- 

chap, i.j Continued identity of Judgment, 89 

ment ; but this only means a bona fide extension of the 
previous whole, such that, if taken in abstraction from the 
process that generates it, it would appear a perfectly new 
judgment. At least in elementary cases it is easy to see 
how inevitably inference shrinks up into single judgments, 
if we look at the actual life of thought. 

Take such an every-day judgment of mixed perception 
and inference as ' He is coming downstairs and going into 
the street.' It is the merest chance whether I break up 
the process thus, into two judgments as united by a mere 
conjunction, or, knowing the man's habits, say, when I hear 
him half-way downstairs, ' He is going out.' In the latter 
case I summarise a more various set of observations and 
inferences in a single judgment ; but the judgment is as 
truly single as each of the two which were before separated 
by a conjunction ; for each of them was also a summary of 
a set of perceptions, which might, had I chosen, have been 
subdivided into distinct propositions expressing separate 
judgments ; e. g. ' He has opened his door, and is going 
towards the staircase, and is half-way down, and is in the 
passage/ etc. If I simply say ' He is going out ' I am not 
a whit the less conscious that I judge all these different 
relations, but I then include them all in the single systematic 
content ' going out.' ' Cromwell Road runs east, and the 
Brompton Road north-east,' are two judgments ; but if the 
road happens to be thought of qua continuous, one would 
say, ' Cromwell Road turns from east to north-east, where 
it becomes the Brompton Road.' Again, ' Knightsbridge 
and Kensington Gore run east ' may be generalised as 
' The street from Kensington Church to Knightsbridge 
Barracks runs east.' 

Thus a judgment is one in respect of the continued 
identity of its Subject and Predication, and this identity 
cannot be defeated by the inclusion of difference, but only 
by the failure to recognise continuity. It is obvious that 
the generalised forms in the above instances presuppose a 
work amounting to colligation of facts, if not to elementary 

90 Judgment a,7id Judgment-forms. [booki. 

induction and analogy. If the included judgments were 
never separately made, the inferential work of colligation 
has not been explicitly done ; but it would be found abso- 
lutely impossible to draw the line between cases where it 
has been done and those where it has not. Every judgment 
would on scrutiny reveal differences which had more or less 
been absorbed into its formation. It follows inevitably 
that every systematic inference considered as a judgment is 
single and not multiple. However this may be, it is clear 
that extension in time is no bar to the unity of judgment. 
Scheme of n. Judgment, as we have seen, is primarily the intel- 
ment of lectual act which extends a given perception by attaching 
Judgments, ^g CO ntent of an idea to the fact presented in the percep- 
tion. The whole of consciousness, in as far as it is the 
consciousness of a single world that shares the reality of 
our Waking self, may be regarded as a continuous judg- 
ment, which qualifies our present feelings and surroundings 
by the knowledge of what is more remote in space and 
in time. From the point of view of common logic, that 
is of individual knowledge, the intellect sustains its world 
by continued effort, as Atlas held up the sky. Every 
judgment is an effort of this kind, affirming on the one 
hand that the same reality which we touch in the present 
is rightly described by such and such an idea, and on the 
other hand that such and such an idea is real with the 
same reality as that which we touch in the present. The 
' idea ' of which I am speaking is, of course, not the par- 
ticular existence or single occurrence of a psychical image ; 
it is the general signification for the sake of which we use 
the psychical image. 

The object of this Book is to analyse judgment into its 
principal kinds, and, as a necessary consequence, to trace 
their affiliation. We shall find that no linear arrangement 
will represent these affinities. Judgment, as the effort of 
thought to define reality, must vary with the kinds of 
reality to be defined no less than with the degree of its 
success in defining them. An equation is to one kind of 

chap, i.] Linear series inadequate, 9 1 

whole what a definition by genus and species is to another, 
or an appreciation of aesthetic value to a third ; the function 
of judgment is present in each of these activities, and the 
difference between them is the difference of the wholes 
which they respectively analyse. They are divergent 
developments of the same relation, in each of which an 
aspect has become predominant that remains subordinate 
in the others. 

But we shall have to deal with convergence no less than 
with divergence. The unity of the judgment excludes no 
complexity of synthesis, and in determining the species of a 
>lant or the character of a man we may be obliged to 
employ, among others, accurate determinations of number, 
time, and space. That is to say, the treatment of a content 
by abstraction as a spatial or numerical whole may be re- 
absorbed in a more concrete treatment of it as an organic, 
aesthetic, or moral whole. 

It might indeed be urged, from the point of view of meta- 
physics, that every kind of judgment must have its value 
and no more as a contribution to the whole of Reality, and 
that therefore the series of judgments, arranged according to 
the degrees of their significance for knowledge, must after 
all be linear. In other words, if a whole in number or a 
whole in space is not final in itself, but demands something 
further to complete its significance, this might be enough to 
show that we ought not to represent it as the goal of an 
independent series, but rather as a stage or phase of con- 
struction, subordinate to the more concrete forms of know- 
ledge K I should not greatly object to such a view, and 
shall endeavour in some degree to meet its requirements by 
exhibiting the more complete and concrete syntheses as 
involving the reunion of aspects which have been developed 
in the abstract. But though the forms of space and time 
are involved as a fact in the perceptive construction of the 
world of individual things, yet the mathematical analysis of 

1 Cp. Plato's arrangement, in the Republic, of the mathematical sciences in 
an order proceeding from abstract to concrete. 

9 2 

Judgment and Judgment-forms. [book i. 

these forms is an effort of the same scientific spirit which 
recognises the principles of order in the world of things 
itself. The two aspects of constructive science are co- 
ordinate and complementary activities of reason, and it 
would be ridiculous to treat geometrical analysis as prior to 
the perception of characteristic size or proportion. Intelli- 
gence is many-sided, in spite of its unity ; and its aspects, 
which are correlative to each other, lose their true inter- 
dependence by being drawn out into a linear series. 



Rudimentary or Intermediate 
Series of Judgments. 

(Judgments of Quality.) 
Impersonal Judgment; 
Demonstrative Judgment ; 
[beginning with ' this,' ' here,' etc.] 
(Judgments of Quantity.) 
Comparative Judgments, etc. 
(Judgment of Proportion.) 
Measurement, etc. 

Abstract or Hypothetical 

Concrete or Categorical 

(Singular Judgments.) 
Individual Judgment, etc. 

(Universal Judgments.) 
Quasi-collective Judgment. 

True Generic Judgment. 


(Enumerative Judgments). 
Plural or Particular Judg- 
Collective Judgments. 
Abstract relations of Space 
and Time. 

Hypothetical Judgment. 

Disjunctive Judgment. 

Infinity in Space and Time 

Purpose of 

i. I subjoin a scheme of the arrangement which I pro- 
pose to follow in the remainder of the present Book. It is 
simply intended to assist the reader in apprehending the 

Chap, i.] Innovations in scheme. 93 

views which I submit, and is not meant to be a bed of Pro- 
crustes for the facts of logic. I take it that variations of 
arrangement and nomenclature are as inevitable in logic as 
in botany, and are not undesirable in either science ; for 
they force upon our minds the truth that species are but 
sections of evolution, and that their arrangement is merely 
subsidiary to a correct apprehension of the process which 
we divide into such intervals. 

ii. I will begin with a few words in explanation of the Explana- 
scheme which I have adopted. scheme. 

There is no need to apologise for describing some 
types of judgment by appellations which are not to be 
found in Mill, Whately, or Hamilton. Recent attempts to 
restore to logic its hold on living concrete thought, a direc- 
tion in which Mill was himself an able and adventurous 
pioneer, have made us familiar with a whole chaos of psy- 
chological, grammatical, and quasi-mathematical titles ap- 
plied to phases of the judging activity. All that I have 
done has been to concentrate in a single review the best 
estimate that I could make of the typical character and 
true affiliation of such phases, attempting to give each 
judgment its appropriate place in relation to all the prin- 
ciples employed in the classification, and eschewing the 
too common habit of adducing various groups and appel- 
lations in two or three successive chapters, without any 
distinct reference of the one grouping to the other. 

But besides adding to the traditional scheme of judg- 
ments, the arrangement suggested involves a dislocation of 
its parts, and the omission of one familiar antithesis. These 
innovations, though by no means original 1 , may conveniently 
be indicated and justified in a few introductory remarks. 

a. ' Categorical ' and ' Hypothetical ' are taken to desig- Categori- 
nate fundamental characters of knowledge, and not mere Hypo- 
grammatical appearance. It follows that the natural series thetical. 

1 The treatment of the universal judgment as fundamentally different from 
the singular in categorical character was really initiated by Mill in so far as he 
analysed the content of affirmation into coexistence of attributes ; and has 
been adopted and accentuated by Lotze, Sigwart, and Bradley. 

94 Judgment and Judgment-forms. [booki. 

of judgments commonly known as singular, particular, and 
universal, cannot wholly fall within the genus categorical, 
but at a certain point and in a certain degree assumes a 
hypothetical character. More especially, the formal equi- 
valence of the singular to the universal judgment is replaced 
by a profound distinction of kind between the two. The 
disjunctive judgment again has a place and value of its own, 
and is not a mere proposition or grammatical form. 
Divergent /3. The true quantitative judgment not the ' universal ' 
species. judgment of ordinary thought, which derives only its name 
from quantity reveals itself as a divergence from the central 
development of the judgment by reason of its extreme 
abstraction, in which one element of the relation essential 
to judgment almost disappears. 
Analytic y. The familiar terms f analytic ' and ' synthetic ' are not 
s^th . made use of in the classification, because they belong to 
the theory in general and are not distinctive of any par- 
ticular types. 

I subjoin a short explanation on each of the above 
Categorical a. A categorical judgment asserts an actual fact abso- 
theticaL 30 " lutely. A hypothetical judgment asserts only the conse- 
quence that follows on a supposition. The distinction 
between the two seems clear. It is the difference between 
' There is a bad smell in the house ' and ' If there is an 
escape of gas there will be a bad smell.' But when we 
come to the ' Universal' Judgment the line of demarcation 
is at once blurred. Hamilton gives ' Rainy weather is wet 
weather ' as an instance of a categorical proposition, and 
1 If it rains, it will be wet ' as an instance of a hypothetical. 
In the former, according to him, ' rainy weather ' is ' un- 
conditionally thought to exist.' But is it ? Prima facie 
the two propositions represent the same judgment, that is 
to say, their difference is grammatical only, and their 
meanings are identical. It may be that the categorical 
shape conveys a presupposition which is absent from the 
hypothetical enunciation the presupposition that rainy 

chap, i.] Abstract is Hypothetical. 95 

weather exists in rernm natura and into the question 
thus raised we shall have to enter at length later on. But 
it is clear at all events that the ' categorical ' form conveys 
in this case a meaning which is in a. large measure, if not 
entirely, hypothetical. 

By referring to our account of judgment as such we 
shall see that the distinction before us involves a funda- 
mental difficulty. Every judgment affirms an idea of 
reality, and therefore asserts the reality of an idea. Now 
an idea is necessarily abstract, because determinate ; and 
therefore all judgment involves abstraction. And abstrac- 
tion is the essential element of hypothesis ; it consists in 
taking up into an idea some elements out of the content of 
experience, for the sake of consequences which attach to 
the elements so taken up. Therefore it seems, as the real 
world for us is maintained and extended by Judgment 
only, that in all extension and even maintenance of the 
given reality there is involved an element of abstraction, 
which is the same as to say that in all categorical judging 
there is an element of hypothesis. The relation of these 
characters to each other throughout the history of the 
judgment will be the main principle of the evolution which 
I shall attempt to describe. But we must accept as the 
usage of thought, which we are to explain, that the assertion 
of actual fact coincides as a rule with the individual or 
singular judgment, and that the universal affirmative of 
formal logic, on the other hand, may in every case be taken 
as purely hypothetical. 

The categorical character of a judgment in the above 
simple sense may be tested by the possibility of expres- 
sing its meaning by an impersonal proposition, however 
awkward may be the necessary grammatical transforma- 
tion. For ' Caesar was crossing the Rubicon ' we may 
substitute ' There was Caesar crossing the Rubicon ' ; but 
for ' All men are mortal ' it is impossible to frame such 
an equivalent, for the reference to given reality in the 
impersonal expression would be at once contradicted by 



96 Judgment and Judgment-forms. [Booki. 

the abstract ' all,' which = c any or * if a-/ and so points, 
in the absence of any more effective assertion of the limited 
unity of the race, to an infinite series. If it is possible to 
say ' These are all the men who, etc., etc.,' the ' all ' cannot 
be the true generalising ' all,' but must indicate a sum of 
known individuals. It will be necessary however to point 
out hereafter that the distinction between these two senses 
of ' all,' or in other words the limit of individuality, is not 
absolute, but is a matter of degree. 

These instances suggest the principle to which we shall 
adhere, viz. that every assertion is as absolutely categorical 
as the nature of its elements will permit ; and that demon- 
strative or individual judgments are in the plainest sense 
categorical, because the realities indicated by their subjects 
are of a nature that can be given, in a way in which the 
realities indicated by more definite abstractions cannot. 
In every case the real subject is the reality indicated ; in 
every case this subject is alleged to exist ; but the question 
is how and in what way it is capable of existing ; in other 
words, what is the kind and degree of its individuality. 
For only what is individual can have actual existence as a 
whole. An infinite series cannot have such existence, and 
therefore cannot be taken to have it. The ' all ' in this 
latter case remains a demand with which we cannot comply. 
Divergent (3. The content of a judgment is always a significant 
idea, that is to say, a recognised 1 identity in differences. 
The varieties of judgment correspond to the forms which 
identity in difference is capable of assuming. 

An identity in relation to its differences may always be 
regarded as a whole in which they are parts. An expanse 
of the same colour includes the changing lights and several 
points of space through which the one identical colour 
extends ; the policy of a government includes the details 

1 ' Recognised ' is necessary to restrict the description to significant ideas. 
For a sequence of images in elementary reproduction, such as we ascribe to the 
animal mind, is an identity in difference, though we do not suppose it to be 
an objective reference, i. e. a recognised identity. See Bk. II. chap. i. sect. 3, 
The Reproduction of Ideas. 


chap, i.] 'Analytic' and 'Synthetic! 97 

into which its principles are developed ; the moral character 
of a man is a whole in which his several acts of volition are 
the variously dependent parts. In this wide sense, as a 
synthesis of differences, not as a sum of units, the relation 
of whole and parts is a fundamental relation of all judg- 
ment. It is only when the differences or parts assume the 
maximum of homogeneity, and conceal, so far as is possible, 
the individuality of their relations to the whole, that the 
parts become units, and the whole a total or a sum. The 
relation of unit to sum total, that is, of quantitative part to 
quantitative whole, is thus obtained by abstraction. It is 
not the complete natural relation of concrete identity and 
differences, but is a device of knowledge which by sinking 
all other aspects of a given content is enabled to regard it 
as a sum of units, that is to say, as a whole of magnitude. 

For this reason it seems right to consider the judgments J 
of number, with the kindred judgments of magnitude in 
space and duration in time, as belonging to an outgrowth 
of thought which diverges from the complete evolution of 
judgment. All these judgments begin as qualitative, but 
become quantitative by intentional abstraction, and end in 
the creation of ideal totalities (abstract number, abstract 
space, abstract time 1 ) which we are unable to think of as 
complete, and therefore are debarred from treating as 
actual totalities. This, I may point out, is a case of the 
connection between individuality and actual existence, 
which I spoke of under the last head. 

y. Every judgment is both analytic and synthetic. This Analytic 
would not by itself be a sufficient ground for refusing to thetic. yn 
employ these terms as heads of classification, for it is more 
or less the case through the whole of Logic that terms must 
be employed to mark predominant aspects rather than ex- 
clusive characters. Nor do I find a sufficient ground of 
objection in the psychological comment that the judgment 
which adds a fresh predicate to a subject to-day must 
become tautologous or analytic if repeated to-morrow, and 

1 Cp. Locke's Essay, II. xiv. 31, on 'Duration.' 
VOL. I. H 


98 Judgment and Judgment-forms. [booki. 

that therefore it merely depends on individual knowledge 
and memory whether a given judgment is synthetic or ana- 
lytic. Any conception of dominant quality, function, or 
essence, is enough to make this comment futile, and without 
such a conception it would seem that science is impossible. 
It is a superstition to suppose that the progress of theo- 
retical explanation in terms of general law threatens the 
doctrine of essence, form, or function. However clearly an 
individual thing may be explained as a section of evolution 
or a meeting-point of forces, there will always be a definite 
continued identity conferred by characteristic form or 
function. No explanation can destroy the actual relations 
of whole and parts which form the essence of everything 
that is real. Knowledge has quite enough fixity to give 
meaning to the contrast of analytic and synthetic judgments 
wholly apart from the progress of individual minds. 

The reason why I no longer care to lay emphasis on the 
antithesis in question is not that it is purely 'subjective' 
for this is not the case nor even that it is only a distinc- 
tion of degree for that is the character of most distinctions 
in Logic ; but simply that it is not a sufficiently specific 
antithesis to be of practical value in classification. I sup- 
pose that if the terms were to be employed, we should call 
those judgments analytic which attain to an adequate ex- 
planation or appreciation of a complex whole. The best 
instances might be the definition or the disjunction, the 
equation, and judgments passed upon moral and aesthetic 
value. In all these cases we have the whole completely 
given in its parts, the identity in its differences, and there- 
fore we are entitled to consider not so much the nature of 
the whole reconstructed, as the exhaustiveness of the re- 
construction. But, as the above instances show, adequacy 
or exhaustiveness exhibits itself in contents whose nature 
is wide apart, and therefore it has no convenient place as a 
general character in a classification. 

On the other hand, as terms belonging to the general 
theory of judgment, analytic and synthetic are of profound 

chap, i.j Parts and whole. 99 

significance. I said at the beginning of this section that 
every judgment is both analytic and synthetic. This asser- 
tion demands no explanation, if we remember our account 
of judgment as always involving identity in difference. But 
I will attempt to illustrate its meaning more fully. 

If I say ' Caesar crossed the Rubicon,' I start with an 
individual Caesar, whose continued identity extended 
through a certain space of time and revealed itself in a 
variety of acts, and I exhibit his identity in one of the acts 
and moments its differences through which it persisted. 
What I mean by the affirmation is that he, the Caesar 1 who 
had before conquered Gaul, and who was afterwards mur- 
dered on the Ides of March, displayed his character and 
enacted part of his history by crossing the Rubicon. This 
is a clear case of exhibiting an identity in difference. But 
the process has inevitably two aspects. On the one hand, 
I analyse the individual whole that is called Caesar by 
specifying one of the differences that may be considered as 
a part within it ; on the other hand, I construct or make 
synthesis of the individual whole in question, by exhibiting 
it as a whole that pervades, and absorbs in itself, each or 
all of its differences. It is only an individual whole that / ^j 
is obviously present in each as well as in all of its differ- / 
ences, as the individual Caesar in the act of crossing the 
Rubicon. A totality whose unity is incomplete, such as f 
1 all men,' is only implied in each of its differences, and is 
not given as a whole in anything short of all. But this 
does not alter the fundamental nature of assertion. Every 
judgment exhibits a whole in its parts, and parts as con- 
tributory to a whole. 

Much has lately been said of Kant's celebrated instance, 
the equation 7 + 5 = 12. We have here a total, twelve, 
which can be compounded in a variety of ways if we con- 
sider numbers larger than twelve, and permit subtraction, 
in an infinite variety of ways and we display this total as 
identical, whether expressed by its place in the series of 

1 Contrast Lotze, Logik, sect. 58.^ 

H 2 

i oo Judgment and Judgment-forms. [book i. 

numbers (which implies one and the simplest mode of its 
formation) or treated as the sum of two other totals, each 
of which is expressed in the same simple way. It is 
obvious that if analytic and synthetic were reciprocally 
exclusive characters, the question ' Is this equation an 
analytic or a synthetic judgment?' would be wholly un- 
answerable. If 12 were not the same number as 7+5, the 
judgment would not be true; if 7+5 gained nothing by 
being defined as 13, the judgment would cease to be 
a judgment at all. 7 + 5 is one of the differences which 
constitute the nature of the total 12, and by constructing 12 
in this way we ipso facto analyse it. ^/ 

The relation of these two processes, or rather two aspects 
of the same process, is so fundamental in all knowledge, being 
in fact the relation which especially characterises knowledge 
as such, that I may be pardoned for continuing to insist on 
it by help of another set of considerations. The notion of 
a plain difference between taking to pieces and putting 
together arises from actual operation on material things. 
This origin of the metaphor involved in 'analysis' and 
' synthesis ' has reacted and still reacts injuriously on our 
conceptions of intellectual processes. In mechanical opera- 
tions we cannot pull to pieces and put together the same 
thing by the same act, and which of the two we can do is 
determined by the material handed to us. If a thing 
is complete already, we cannot put it together any further ; 
the only alternative then open to us, as between these two 
processes, is to pull it to pieces; and so vice versa. But this 

! feature of material operation cannot be transferred to 
thought, and for this reason, that the essence of thought 
is to show the process in the result, and exhibit each as 
necessary to the other. Therefore, if we construct in 
thought, the materials out of which we construct have not 
lost their separateness when the fabric is finished ; the 
fabric as it is still issues from them as they were ; if not, we 
have dropped a link, and our construction is unwarranted. 
y The synthesis, one might say, is based on the analysis ; 

chap, i.] Synthesis in fact and in thought. 101 

but this would ascribe a false priority, because the fragments 
supplied to us only become an analysis as the synthesis, 
which relates them to a whole, progresses. Apart from the 
synthesis they are mere fragments, and therefore are not an 
analysis of anything. The workman who puts together the 
parts of a watch has first the handful of wheels and springs, 
and then the completed watch ; he cannot have both at 
once, and in as far as he has one he has not the other. 
Moreover, when he has made the watch the wheels and 
springs are together and are not separate, nor are they separ- 
able consistently with the existence of the watch. Synthesis 
in this sphere is incompatible with analysis, and vice versa. 
But a man who wishes in thought or calculation to construct 
any instrument out of parts has a very different task. Every 
element of the handful of parts must have its place and 
functions clearly retained in the intelligence which constructs 
the whole ; for the whole, as a whole of intellectual synthesis, 
exists no longer than its parts are clearly apprehended in 
their relations. ' Yes,' it may be said, ' but the distinction 
must remain that even in thought you may either begin by 
considering detached wheels, etc., and finding out how they 
must act in the watch, or by looking at a watch and 
detecting, within its completed system, the separate parts 
and their relations. The former process is synthesis, 
the latter analysis.' 

This is true so far as judgment or inference is an 
activity in time, and includes within itself a transition in 
time. In so far as it has this character, the process of 
thought can simulate or share the characteristics of 
material operation. But this does not affect the internal 
nature of judgment, as I have pointed out in discussing its 
temporal character. The question is not whether you begin 
with the whole or with the parts, but merely what sort of 
whole and what sort of parts you begin with. Given an 
escapement wheel, I may chance even to be ignorant that 
it belongs to a watch at all ; but none the less I judge of it 
as a part in a whole, which whole I can at first only think 

102 Judgment and Judgment-forms. fBooKi. 

of, perhaps, as ' some piece of mechanism that depends on 
a catch playing into a delicately toothed wheel. 5 The further 
intellectual construction of this mechanism and the ultimate 
definition of it as a watch, is, according to the views of the 
passage just referred to, not a transition from 5 to P, but a 
transition from the judgment s-p to the judgment S-P. We 
therefore find analysis no less than synthesis to be the internal 
essence of every minutest section of the judgment or inference 
in question. In the same way, if a watch is put into my hand 
with instructions to find out what makes it go as it does, I 
have primarily a thing in space as the given whole, and in- 
definite wheels, springs, etc. (which as yet I cannot distin- 
guish by position or characteristic shape) as given parts. No 
doubt in space all the parts which I shall need to learn are 
given in position within the whole, and so we tend to describe 
the problem as one of analysis, in contrast to the other (in 
which I had to find out or imagine the position of the parts 
in the whole) as synthesis ; and these titles serve well 
enough as superficial descriptions of certain cases to which 
judgment and inference are applied not of any judgment or 
inference as such. But the whole is not, in the latter case 
any more than in the former, given as an intelligible machine, 
nor are the parts given within the whole of knowledge 
because they are within the whole of space. In other 
words, to see the escapement wheel lying inside the watch 
does not ' give ' me this wheel as a part of a mechanical 
arrangement ; to know it as a part of such a whole I must 
understand it ; and in understanding it, i. e. in my analysis, 
perform the synthesis of the watch as a definite mechanical 

Therefore not only is every judgment both analytic 
vand synthetic, but it is analytic only as far as it is syn- 
'thetic. It can only be called analytic or synthetic par 
excellence if, by the same confusion that causes the judgment 
to be regarded as a transition from 5 to P, we consider 
the joint analysis and synthesis of one whole as the ana- 
lysis or synthesis of another; because in that case we 

chap, i.] Analytic or Synthetic par excellence. 103 

seem to have a fixed and given whole, and to predicate 
of it nothing but parts, or vice versa. In this confusion 
there is an element of truth. Though s must become 5 
when/ becomes P, yet s has continued identity with S and 
p with P, and therefore the transition in time from s-p to 
S-P does all that could be done by the unreal transition 
from s to P. Present me with a pattern s which is a tissue 
of intersecting curves /, and when I have analysed it into 
the thistle design P, the pattern s is transformed to my eye 
into a distinct and beautiful design 5 ; but 5 is the same 
that was s, and in that sense we have connected s with P, 
and we may represent P as the analysis of s, only not for- 
getting that it is the synthesis of 5 which is the same as s, 
and that therefore in predicating P of s we ipso facto trans- 
form s into 5. And thus the complete understanding of a 
watch as a mechanical system, expressed in the joint 
analysis and synthesis S-P, may be accepted as happening 
to involve, par excellence, either the intellectual analysis of 
the watch as a given whole in space s, or the intellectual 
synthesis of the watch out of given separate parts in space 
s v s 2 , s 3 , etc. The given whole, or given parts, can be 
thus allowed to pass as merely whole, or merely parts, 
because they are not respectively whole and parts in the 
sense contemplated by the judgment S-P, and therefore it 
does not press home their relation to one another. The 
watch seems to be from the first a ready-made whole, a 
round thing s in space, which can only be analysed, and 
not constructed, by the judgment S-P. But it is further 
constructed, not as a round thing in space, but as a 
mechanical system, by means of that judgment. 


Quality and Comparison. 

I NOW turn to examine specific types of judgment; but 
in doing so, I must beg leave to remind the reader of 
the principle which I have laid down as governing any 
enquiry into a continuous development \ What we wish to 
master is the nature of a process, the scientific history of a 
function. To do this, we must of course study and arrange 
its detailed manifestations ; mere generalities are valueless. 
But we need not be disheartened if our subdivisions and 
specific names are different here and there from those 
adopted by better authorities, nor even by the possibility 
(which can hardly be absent from a highly detailed treat- 
ment) that we may misinterpret some phase of evolution, or 
lay down some inconvenient demarcation. If the main 
problem is thoroughly faced, and the analysis of some chief 
typical forms accurately conducted, the reader will be in a 
position to correct blunders and to supply omissions by the 
light of the knowledge so gained. If we can help him to 
sound principles and practice of morphology, he will make 
short work of particular varieties of type. 

Judgment, we have seen, is, speaking generally, the 
intellectual function which defines reality by significant 
ideas, and in so doing affirms the reality of those ideas. 
I use the term 'define,' because to define implies some- 
thing given which is to be defined ; and it is an essential of 
the act of Judgment that it always refers to a Reality which 
goes beyond and is independent of the act itself. 
The Judg- i. We will now look at the judgment in its simplest form, 
Quality, which I have ventured to call the Judgment of Quality, and 

1 Vid. Introduction, p. 16. 

Qualitative Content. 105 

which, with its immediate sequel, the Judgment of Com- 
parison, finds linguistic expression in the Interjectional or 
Impersonal Proposition. 

i. By Quality I understand, not all attributes without Meaning of 
distinction, but the unanalysed content of any idea, when ^ ua lty ' 
treated, in its unanalysed simplicity, as a feature of reality. 
It may be that all qualities are capable of being analysed 
into relations ; but for our present purpose the question is 
not whether a quality can be, but whether it is so analysed. 
Even the diagrams familiar to us in Euclid, which exist for 
the very purpose of being analysed, have each its peculiar 
look or effect, lopsided or symmetrical, solid or slender, 
circular or bristling with angles. Qualities of shape, how- 
ever, are A a rule quickly analysed into relations of propor- 
tion, so that the commonly cited phenomena of colour and 
sound give better instances for our purpose, while percep- 
tions which are named, like softness and sweetness, with 
some reference to pleasure and pain, are the best instances 
of all. It might indeed be suggested as a definition of V 
quality that it is that aspect of any perception or idea in 
which it gives rise to pleasure or pain. 

ii. The Qualitative Judgment proper affirms a nearly Judgment 
simple content directly of present Reality. An absolutely proper/ Y 
simple content is indeed an impossibility ; every ' red ' or 
1 sweet ' or ' pleasant ' belongs to some context and includes 
some differences. But, as I have attempted to explain in 
the last paragraph, a qualitative content is very nearly 
simple. The context which makes its difference is the 
context for the sake of which we affirm it, and is thus pre- 
supposed, and not itself affirmed as a further complication. 
If I exclaim ' How hot ! ' I do so because the weather or the 
room is hot, or perhaps if I am feverish, because I am hot 
for no obvious reason. In all these, no doubt, the content 
{ hot ' belongs to something ; it is not isolated from the varied 
surroundings of my position, but exists in and extends over 
some of them. But I affirm it without specification, or 
rather as a first effort to make specification, of my position 

106 Quality and Comparison. [booki. 

and surroundings in general, and neglect to analyse its rela- 
tions, or only analyse by implying that it has some relation 
or other. 

Thus much for the Predication. As for the subject of 
a pure Qualitative Judgment, there is prima facie no assign- 
able subject within the judgment. No ideas are employed 
to limit the aspect of reality to which the predication refers. 
The whole of what is perceived at the moment, or more 
probably some unspecified aspect of it or element within it, 
is the subject, and it is of this that the content is affirmed. 
By 'unspecified,' I do not merely mean unspecified in words 
spoken aloud, but undefined by any such act of conscious- 
ness as employs symbolic ideas and tends to call up words. 
But if thus unspecified, how can the subject be indicated, 
limited, or selected ? I answer, simply by the concentration 
upon' it of perception or attention, the exclusive gaze which 
might be represented by pointing with the finger, and which, 
though it has limits, is definitely aware of none. In this 
sense, confining what is ' present to perception ' within the 
limits of what more especially arrests attention and is 
taken as ' This 'par excellence, we might say that the subject 
of the Qualitative Judgment is always the whole of what is 
present to perception. 

The best illustrations of this rudimentary Judgment are 
drawn from significant Interjections, or from significant 
phrases used as Interjections. A distinction must be observed 
between the true Interjection \ the outcry which relieves the 
urgency of feeling, and the affirmation which refers the con- 
tent of feeling as a quality to the surroundings that evoke 
it. The cry of an animal is often significant for us ; it tells 
us what the animal feels, and why ; but we do not therefore 
reckon it as the expression of a judgment. What makes 
the judgment is the idea that exists in our minds and yet 
that only has truth as referred to Reality. And therefore 
if we doubt whether we have a judgment before us, we 
should ask if it is anything that could intelligibly be denied. 

1 Cp. Lotze, Logik, sect. 48. 

chap, ii.] Interjection and Judgment. 107 

It is impossible to deny the animal's mere expression of its 
feeling ; and although we may see a reason for its feeling 
which we know to be an illusion (e.g. if a dog barks joyfully 
in expectation of being taken out, when he is not going to 
be), yet there is nothing which we can deny unless we can 
suppose that this illusion exists in the animal's mind as an 
idea distinguished from and referred to reality. If we could 
believe this to be so, we should have to admit that the 
animal judges. But short of this, there is nothing to deny. 
The dog sees me take my hat and stick, he has a set of 
mental images connected with going out, and he expresses 
pleasure. I cannot deny that he has the images or that 
they give him pleasure. It would be only if he could take 
these images as standing for something other than them- 
selves, and so distinguish their meaning, a future event in 
reality, from their existence, as present images in the mind, 
that anything could possibly arise which I could intelligibly 
deny. The ideas used in judgment must exist before they 
can be denied, and therefore their existence cannot be denied, 
but only the affirmation of their meaning \ 

Coming to human interjections, we might think that 
1 Alas ! ' characterises the present as grievous ; and it is 
certainly sometimes answered, though hardly denied. But 
the answer, even if it takes the form of a denial, is usually 
rather prohibitive (imperative) than negative ; though if self- 
deception or hypocrisy are suspected, ' alas I ' may be inter- 
preted as ' I am sorry,' and in that sense denied. The 
distinction to be kept in mind is here one degree more 
subtle than in the last case, for the objective content of the 
judgment is the fact of a feeling in the mind of the person 
who judges. Thus we have, if ' alas !' is a true interjection, 
the emotion of grief present in the mind of the person, 

1 These remarks are made purely for the sake of illustration. I have not the 
least prejudice against admitting that animals can judge, if the admission can be 
warranted by fact, and does not involve truncating the theory of judgment. 
Domestic animals certainly seem to use the imperative, i. e. to insist on the 
realisation of their ideas. Cp. Bradley, Principles of Logic, p. 33. 

108 Quality and Comparison. [booki. 

which merely forces him to utterance by way of relief. But 
if it is to be taken as a judgment, then we have in any case 
the symbolic idea of sorrow, existing in psychical images, 
but having its meaning beyond them, and a reference of 
this meaning to the present perceived being of the person 
in question. And above all this, if the judgment is true, 
there must be, as before, the actual felt emotion of sorrow, 
though if it is false, this element of the complication is 
absent. It is possible that this peculiar complication, of the 
idea with the actual feeling behind it, is responsible for the 
curious duplication of personality which is sometimes ex- 
perienced in protracted pain or anxiety. The person whom 
we analyse and judge seems other than the person who all 
through the process has the feelings which are being 
analysed, or rather are forcing their disagreeable peculi- 
arities on our attention. ' If / were suffering so, how horrible 
it would be,' we repeat to ourselves. Just as the comple- 
mentary image comes between our eyes and the sun, so the 
idea of our feeling comes as the object of knowledge between 
us and the feeling itself, which remains in the background 
and resists our successive efforts to include it in an adequate 
idea. The sufferer remains to us distinct from the person 
whose suffering we conceive and affirm. 

However this may be, when we come to such quasi-inter- 
jectional expressions as ' Bad ! ' ' How ugly !' ' Such pain ! ' 
' Oh horrible ! ' we are unquestionably dealing with judgments. 

The Impersonal Proposition is also a suggestive counter- 
part of the judgments in question, which have even been 
treated as Impersonal Judgments. But the impersonal form 
of sentence has become in developed language so purely a 
grammatical fiction, that it no longer illustrates with special 
appropriateness any one type of assertion ; although it 
exhibits a certain coincidence with the range of the concrete 
existential or singular categorical judgment. 

A few instances however occur to us at once and 
philology might be able to furnish more of impersonal 
sentences that really seem to have stood for judgments 

chap, ii.] The Impersonal Proposition. 109 

whose subjects were not especially designated by means of 
ideas, but were accepted as merely the given in perception. 
Such may be ' Methought,' 'Him list,' 'Mir traumt's 1 ,' 
1 Es trieb mich,' - Taedet,' ' piget,' etc., ' It rains,' ' es macht 
heiss,' vet. As, in the plastic Greek imagination, Athene 
may suggest a man's thought, and the actual Dream stand 
over him in sleep, so, it would seem, in the beaten track of 
language, the thought and the dream are simply referred to 
* it ' or to * something ; ' to the present reality or to an in- 
definite element within it. Though the formed verb pre- 
supposes a distinct reference of ideal contents to real 
subjects, yet the habitual use of expressions in which this 
reference is blunted and neutralised, testifies to a survival, 
in certain preeminently obscure relations, of a rudimentary 
type of judgment. This, I think, is the only connection 
that we can safely assume between the Judgment of Quality 
and the Impersonal Proposition. 

The Qualitative Judgment is the_ germ and simplest case 
of the Perceptive Judgment. Perception is a wide word, 
including, as frequently used, any so-called immediate 
apprehension ; even that, for instance, by which we are 
supposed to see the necessary truth of one of Euclid's 
axioms. But if we are to give the term a distinctive 
logical meaning, we should do well to restrict it to so-called 
immediate apprehension when dealing with the portion of 
reality which is in contact with the individual through the 
senses. Perception thus defined deals primarily with what 
is present, but extends it by ideas which go beyond the 
present. When we recognise a man and call him by name, 
we are said to 'see who he is,' i.e. to perceive. In this 
case our perception is expressed by an idea that goes a 

1 In Greek, a conservative though flexible language, ' I dreamt,' is never, so 
far as I know, impersonally rendered : but on the other hand, in Homer the 
dream is personified. The principle is the same in so far as my dream is not 
referred to me as my act. Indeed the coincidence is curious with the "view of 
those who have held that the subject of an impersonal proposition is the content 
of the verb itself as in ' the rain it raineth every day.' It is much the same to 
say ' Es traumte mir ' and to say A dream came to me.' 

no Quality and Comparison. [booki. 

long way beyond the present and brings in the man's 
entire personality. 

The Qualitative Judgment does not differ from the judg- 
ment which recognises an individual, by being shut up 
within a minute interval of present space or time. It is 
not minuteness of extension or of duration that distinguishes 
the reference of this simplest case of the perceptive judg- 
ment ; the qualitative affirmation may deal with what is 
really a considerable area of space or interval of time. The 
distinction is not one of magnitude, but of definiteness. 
There is always a risk of construing the absence of quan- 
titative determinateness into determinate minuteness of 
quantity. This is just what we want to avoid. The quali- 
tative judgment knows nothing at all of duration or of 
extension, and can have no specified individual for its 
subject. It is thus confined within the' given presentation 
in so far as the universality, whether abstract or concrete, 
is absent that alone could extend it beyond. The Reality 
which is the subject is the given as given, not as a universal 
that reaches before and after ; the content of the predi- 
cation includes no negative element, summarises in itself no 
diverse manifestations, and thus neither refers to anything 
beyond the present, nor in any specific way to the present 
itself. It is attached to the present by the mere fact of its 
actual reference to presentation, not by anything within 
its explicit content. The first specification, the first estab- 
lishment of an identity that can be called by a name, is 
the work of this judgment, and is not presupposed by it. 
We must take it, I think, after the discussions of the 
Introduction, that the establishment of a name a per- 
manent identical symbol of a meaning must on the whole 
have coincided with the establishment of meanings as such, 
distinct from psychical occurrences, and capable of being 
referred to reality. I have attempted in the discussions in 
question to qualify the rashness of this unverifiable 1 his- 

1 Of course there can be verification by analogy ; and it is hard to draw the 
line between this and actual verification. The characteristic cries of animals 

chap, ii.] Analytic and Synthetic Judgment of Sense. 1 1 1 

torical allegation, by pointing out that the two co-ordinate 
processes the constitution of symbolic ideas and of lin- 
guistic symbols must be regarded as processes of gradual 
and unconscious adaptation, widely differing from the 
methodical extension of nomenclature according to modern 
ideas. But the logical track is the same, whether the his- 
torical evolution is quick or slow, conscious or unconscious. 

Perception as above defined would include two species 
which have been called respectively the 'Analytic' and 
the 'Synthetic' judgments of sense. If these distinctions 
are to be seriously treated, and we are to speak of any 
judgments as merely analysing a presentation of sense, 
without going beyond what is given within it, then, I think, 
we must identify the Analytic Judgment of sense with the 
Judgment of Quality. It appears to me quite idle to treat 
a description of an ordinary scene, such as 'The blacksmith 
is at his forge mending the ploughshare/ as a case of a 
judgment confined within present perception. Every element 
of the description is a concrete individual, including innu- 
merable differences, involving elaborate categories, and 
extending indefinitely into past and future. If ever there 
was a constructive or synthetic judgment, this is one. It 
would surely be more appropriate to treat these common 
perceptions, which we deal with lower down, as Synthetic 
judgments of sense, because they interpret what is given by 
ideal contents that go beyond it. And then we might 
reserve the title 'Analytic Judgments of sense' or 'Judgments 
of Quality' for the activities represented by the Interjection al 
and Impersonal propositions of which I have spoken, and 
the true Demonstrative propositions of which I shall speak 

The difficulty of identifying simple forms of judgment is 
intensified for modern reflection by the definite and diverse 
articulation of the elements of modern speech. The lan- 

and children have significance for us, and we cannot suppose that they do not 
react upon the intelligence of those who utter them. It would be far easier to 
understand how animals should acquire language, if, like children, they did so 
in fact, than it is to understand how they stop short of it. 

H2 Quality and Comparison. [booki. 

guages which embody the reflective thought of Europe, both 
ancient and modern, resist the expression of elementary 
perception in two ways. First, for a germinal thought we 
need a germinal word. But the languages which mould 
our ideas have no germinal words. Every word, in the 
language of European culture, is a particular 'part of 
speech.' That is to say, it is adapted to fulfil some one 
function in a sentence, whether substantive, verb, pronoun, 
or conjunction, and, if used alone, has an air of incomplete- 
ness which forces us to ' understand ' supplementary words. 
The existence of the Judgment of Quality is but slightly 
corroborated by the fact that a single word often conveys a 
judgment. Many such single words are conventional sym- 
bols for quite definite sentences. But the judgment of 
which we have been speaking corresponds to a whole 
sentence in the bud, with its differences unevolved. How 
far philology could furnish authentic representations of the 
sentence in such a stage words which are not ' parts of 
speech,' but entire though undifferentiated units of speech 
it is beyond the limits of the present work to enquire. 
Even the verb of ancient Greek or Latin, which required 
no supplementary pronoun to represent its subject, is one 
degree more appropriate for the purpose than any element 
of modern speech. 

And the second difficulty is really a case of the first. 
Most judgments are expressed by help of a verb, and if we 
employ a substantive or adjective alone, it urges us to 
' understand ' a verb. But a verb is in our languages above 
all things a tense ; and for a rudimentary judgment like the 
judgment of Quality, a tense is exactly what we do not 
want, least of all the elaborate duration-tense of the present 
(rpexti, amat, ' he is acting '). We want to affirm neither 
duration nor yet point of time ; we simply want to qualify 
the given by a content, without specific limitation or ex- 
tension. It is true that the logical present, the absolute 
present of the universal judgment, marks no limitation of 
time, and it depends on the nature of the content involved 

chap, ii.] Subject in and outside Judgment. 113 

whether universality of time as an infinite series is asserted 
in such a case. But whether it claims universality in time 
or by negation of time, such a judgment implies the con- 
ception of time as an abstract whole and is posterior 
to this conception, while the reference of which we are 
speaking is prior to the origin of the systematic idea of 

These properties of developed language, and prior to 
developed language it would scarcely be possible to have 
analytical reflection, may be compensated, but cannot be 
cancelled. The fact that sometimes thought is behind 
language, and at other times struggles to pass it (it would 
be hazardous to complete the antithesis by saying that 
thought can really outstrip speech) is a fruitful source of 
misinterpretation. Children learning to speak, or savages 
learning a European tongue, are like the wizard's ap- 
prentice uttering a spell ; they are incapable of grasping 
the significance or controlling the effect of their words. 
And all human beings perpetually oscillate between limits, 
different in every case, on the scale of intelligence ; for not 
only is the student's or politician's world of thought very 
different from that of an illiterate man, but every man 
varies in the level of his intelligence according to momentary 
conditions of interest and capacity. The same difficulties 
of interpretation which are found by a student in the speech 
of a child or Anglicised savage, subsist in a less degree as 
between every man and every other, and as between every 
man and himself. 

Up to this point the constituent elements of the Judg- 
ment have been naked before us. There was the Subject, 
the actual contact in which reality pressed upon our sense- 
perception, and there was the significant idea by which 
we defined it. It is this case that affords the strongest 
support to the view which denies all meaning to the dis- 
tinction of Subject and Predicate, as a distinction of 
elements within a judgment. The Reality to which we 
ascribe the predicate is undoubtedly self- existent ; it is not 

vol. 1. I 

H4 Quality and Comparison. [booki. 

merely in my mind or in my act of judgment ; if it were, the 
judgment would only be a game with my ideas. It is well 
to make this clear in the case before us, for in the later 
forms of the judgment it will be much disguised. Still the 
reality which attracts my concentrated attention is also 
within my act of judgment ; it is not even the whole reality 
present to my perception ; still less of course the whole self- 
existent Reality which I dimly presuppose. The immediate 
subject of the judgment is a mere aspect, too indefinite to 
be described by explicit ideas except in as far as the quali- 
tative predication imposes a first specification upon it. This 
Reality is in my judgment ; it is the point at which the 
actual world impinges upon my consciousness as real, and 
it is only by judging with reference to this point that I can 
refer the ideal content before my mind to the whole of 
reality which I at once believe to exist, and am attempting 
to construct. The Subject is both in and out of the Judg- 
ment, as Reality is both in and out of my consciousness. 
The de- fa We have now to consider a slightly more definite 

monstra- ' 

tivejudg- type of judgment, which we may still rank among the 
judgments of quality, although we can detect in it the 
beginning of a further growth. 

When we say, ' This is hot/ ' Now it is raining,' ^ere it 
is dark,' the demonstrative pronoun or particle designates 
the point in given Reality to which the affirmed content is 
to refer. The point is designated, but seems, prima facie , 
not to be described. The demonstrative has a meaning, 
no doubt, but its meaning seems to consist of a mere refer- 
ence to what is presented before perception, and therefore 
does not seem to introduce any abstract limitation that 
qualifies the given subject. Compare, for instance, ' This 
is hot ' with ' This metal is hot.' The latter judgment may 
possibly be met with ' This is not metal at all,' and by such 
a reply the judgment is cut in two, and the more significant 
half becomes a conditional assertion whose condition does 
not apply to the { this ' in question. But ' This ' alone is on 
a different footing. You cannot say, ' There is no this at 


chap, ii.] Space and Time brought in. 115 

all.' There is always a this, as there is always a that ; and 
the same applies to here, there \ now, and then. 

One of these demonstratives indeed appears at once to 
take us over a boundary. ' Then ' requires a past or future 
tense in the predication ; and in referring to the past or 
future we get beyond analysis of the present, which is the 
province of the analytic judgment of sense. The problem 
is one of real importance, but its point is not where we are 
most likely to look for it. It is not that the Judgment of 
quality refers to a point of time, and that ' then ' takes us 
outside this point ; it is that the Judgment of quality is prior 
to the idea of duration, and that we have now introduced the 
idea of duration definitely into the subject. The effect on 
tense, which happens to be the vehicle of predication, 
produced by taking 'then' as the subject, calls our at- 
tention to the fact that every present includes a past. The 
contrast of ' here ' and ' there,' not happening to affect the 
verb, did not force on our notice the equally real uni- 
versality of the present in space. Every ' here ' is made up 
of ' there's ' as every ' now ' is made up of ' then's.' And / 
thus in designating a given subject as 'now' or 'here,' we 
have unawares included in the subject a ' then ' and ' there,' 
and by introducing universals of space and time have set \ 
our faces to leave the region of the qualitative judgment. 
The demonstratives stand for ideas, and it is therefore 
through ideas that in the judgments now in question we 
refer to reality. But the demonstratives have the pecu- 
liarity that their application cannot be denied, as can that 
of a determinate idea such as metal, and therefore, though 
they characterise the given Reality as appearing in space 
or time, yet they can specify no nexus, introduce no con- 
dition, which may be absent in fact, and through its 
absence may save the judgment from falsity by rendering 
it inapplicable. If heat is not present in the ' this ' to which 
it is ascribed, the judgment 'this is hot' is false without 
reserve ; but if to ' this ' we add ' metal ' then the absence 
in fact of the condition ' metal ' makes the whole judgment 

I % 

1 1 6 Quality and Comparison. [book i. 

ambiguous and inapplicable. Thus we have in the demon- 
strative judgment of quality, as in the simple or pure 
judgment of quality, a perfectly categorical judgment ; 
the Subject must, in its nature, exist, and the Predication 
must therefore be alleged to hold good of actual existence. 
It is noteworthy that of this perfectly categorical judgment 
we cannot say whether the existence of the Subject is 
affirmed or presupposed. Where we are dealing with the 
given qua given, the difference between affirmation and 
presupposition has not emerged. 
The Judg- 2. The contrast between ' now ' and ' then ' suggests to 
Com- us tne consideration of such judgments as are expressed by 
parison. < n ow ft hurts less than then,' ' This is redder than that,' 
' Here it is hotter than there.' The form of these judg- 
ments indicates as their appropriate title the Compara- 
tive judgment, or the Judgment of Comparison. They arise 
naturally out of the Demonstrative judgment of quality, 
because, as we saw in the case of 'now' and 'then,' it is 
impossible to prevent the present subject from revealing 
differences within itself. ' This,' as more clearly defined, 
will display itself as a part, 'not-that' within 'this and that,' 
'now' as a part 'not-then' within 'now and then,' 'here' as 
a part 'not- there' within 'here and there.' The whole, 
when thus resolved, displays differences of quality between 
its parts, or rather the given reality reveals itself as a whole 
for the first time when it breaks up into parts united by an 
identical but varying quality. Even if we forget that the 
' this ' and ' that ' ever entered into a single whole, yet the 
identical quality because of which we compare them contains 
in itself the essential of the comparative judgment, viz. 
the explicit recognition of difference in identity. ' Redder,' 
' hotter,' ' less painful,' are terms that go beyond mere 
quality by introducing the conception of more and less, that 
is to say, the beginning of quantity. I give instances, bracket- 
ing the explanatory words which would be superfluous in 
presence of direct perception, and which belong to a higher 
level of judgment than that which we are discussing. 'This 


Chap, ii.] Comparison involves Quantity. 117 

[paper] is green, and this [part of it] is lighter green than 
that.' ' Now [all to-day] it * hurts less than it did [yester- 
day] ; but [just] now it hurts more than it did [a moment 
ago].' But in cases like these we are apt not to notice that 
we are predicating differences within a single identity, the 
green paper, or the whole of to-day ; though we must be 
aware that we imply them in the comparison of quality. 
And therefore, having pointed out the underlying character 
of such a simple analysis as the above, I will pass at once to 
a case which is one degree more complex, but which dis- 
plays the essence of comparison beyond possibility of 
mistake. I refer to the case in which a given whole of 
perception designated by one demonstrative has parts dis- 
tinguished within it by means of the others, and differences 
assigned to it conditionally upon these distinctions. There is 
no difference of principle between denning 'this,' within 'this 
and that,' and defining it within 'here and there.' The 
only advantage is that a demonstrative of another kind is 
more readily taken as a condition, while one of the same 
kind is apt to be understood as a jump to a wholly new 
subject. We will therefore merely change the parts \ which 
might be new and substantive wholes, into conditions. ' This 
is redder now than it was then.' ' This is hotter in this 
part than in that' ' This [green paper] is lighter here [in 
this part of it] than there [in that].' These instances clearly 
show the primary datum revealing itself as a whole with 
parts distinct yet bound together by a common quality. 

i. Let us now examine the essential nature of the com- Quantita- 
parative judgment in one of the above instances. It is not parison" 
my intention to enter upon the niceties of quantitative com- 
parison at the present stage. 

We will take the instance, ' This is redder now than it 
was then ; ' or in the simpler form, ' This is redder than it 
was.' We will take the Predication first, and then consider 
its reaction upon the subject. 

1 The ' it ' in this instance is on the verge of introducing an identical sub- 
ject. I did not however mean it to stand as a definite subject, but merely as 
the grammatical complement of the impersonal verbs. 

n8 Quality and Comparison. [booki. 

That which is redder is also red. The red and redder 
are both red, and yet differ from each other, not, or not 
merely, in other ways, as in time or place, but in respect of 
their redness. It has been sufficiently insisted on that there 
cannot be difference without some identity, as for instance a 
red and green surface are identical in respect of reflecting 
light. But these, though the same in as far as they reflect 
light, are not the same in the light which they reflect. 
There is a break between the two colours, considered as 
colours 1 , which nothing can bridge, and the immediate per- 
ception of their discontinuity supplies the terms which indi- 
cate the difference between them. The surfaces which are 
both red, but one redder than the other, are separated by 
no such break. If one changes into the other, it does not 
cease to display the same quality that it displayed before. 
- But a quality that changes, and yet remains the same quality, 
has passed into quantity, which might be defined as differ- 
ence, not merely in identity as its meeting point, but con- 
sisting of identity as its material. 

Thus the fundamental identity and difference of judgment 
are specified by the comparative judgment as whole and 
parts in the simplest form of that relation : viz. the form in 
which the whole differs from any part by an interval which 
consists of other homogeneous parts. Parts in this sense 
differ from units only by lack of precise comparison ; but 
precise comparison is posterior to the conception of a whole, 
of which we are just considering the first establishment. 
We do not measure or count until we know of some totality 
that requires definition by these processes. 

The reaction of comparison upon a simple subject indi- 
cated by a demonstrative, that is, on a mere spot or point 
upon which perception is concentrated, is an essential step 
towards the recognition of an individual totality. The 
present of space or time is as we saw in its nature con- 

1 It is possible that, considered as amounts of light, red or green may share 
a continuous element and so have quantitative relation. If so, this is another 
case in point. For the difference is then in respect of the characteristic which 
forms the identity. 

chap. II.] Analysis of the Subject. 119 

tinuous. Therefore the spot or point on which perception 
is fixed, and which we indicate perhaps by ' this,' will un- 
doubtedly exhibit differences under analysis. Such analysis 
is brought to bear by the judgment of Comparison. The 
spot or point 1 in which a change of degree is observed 
forces itself on by that fact from being a mere spot on 
which the eye is fixed to the first stage of individuality as 
a synthesis of differences. Change is not necessary to this 
result, though negation in some form is. The observation 
of parts differing in degree within the spot which we have in 
view is as effective for the purpose as the detection of suc- 
cession within the time which we call 'now.' The mere 
spot fixed by perception begins under such analysis to 
assume the character of a Thing ; and by a parallel process, 
the distinctions of Time and Space begin to emerge as 
parts within homogeneous systems. 

It is obvious that such a point in the evolution of thought 
would correspond to the first distinction of Noun, Finite Verb 
with Tense system, and the more elaborate spatial and tem- 
poral adverbs and prepositions. But it would not be fair 
to test the correspondence strictly by negative instances. 
Language fits thought as a very loose glove ; and if it were 
the case that we could find several languages in which our 
familiar parts of speech, more especially the tense system, 
do not exist, we should still no doubt find that the distinc- 
tions, whose origin we are examining, are represented in 
some other way than by linguistic signs, or are thought even 
if not represented. It would be ridiculous to contend that 
the Chinese do not think of self-identical and independent 
things, even if it is true that their language has no special 
class of nouns substantive. Nevertheless, the contrast of 

1 It is hard to escape the dangerous pitfall of speaking as though there were 
no perception but sight, and therefore as if the germ of the judgment were always 
fixation of the look in space. The focus of attention may operate through any 
sense, and is characterised at any moment by that identity which the judgment 
makes explicit. But the identity is referred in rudimentary judgment not to 
a special content as subject but to what could only be paraphrased as ' That 
which engrosses my attention,' the present feeling which the judgment deter- 
mines into thought. 

120 Quality and Comparison. [booki. 

development between different languages has or has had its 
meaning ; and it appears to me absolutely impossible that 
a people whose sole language was Hebrew could have had 
the accurate consciousness of time as a system which came 
easily to the Greeks and Romans of the classical age. I 
believe, indeed, that the origin of the Aryan tense-system 
is not beyond the ken of philology, and that its probable 
history reveals an evolution much like that which has been 
here suggested a transition from simple unspecified refer- 
ence, to reference differentiated by a temporal system. 

'This,' then, as the subject of a continuous Quality in- 
cluding differences tends to acquire an individual name. 
I have pointed out in the Introduction that the process of 
Naming in a world distinctly organised by knowledge 
cannot be that which belongs to the unreflective epochs of 
thought. A natural name must be a petrified description. 
The linguistic element which stands for the content of the 
Judgment of Quality is already a name. And some such 
element, in the simplest case perhaps that element itself, 
will emerge in later forms as a description of the newly dis- 
tinguished individual, which in the Judgment of Quality is 
only known as ' this.' ' This red (leaf) is redder than it 
was.' And when the individual is once revealed as a 
whole with parts by this judgment of Comparison or syn- 
thetic judgment of sense, the ascription of other differences 
to it cannot but follow. It seems obvious that an adjectival 
appellation, or at least an appellation of unspecified 
grammatical class, would come first, and the hardening 
into a substantive be a later process. I incline to think that 
the hardening of a description by usage, and the isolation 
of its elements by employment in different judgments, 
must have been the real and natural process of naming. 
Com- ii. It is evident that judgments which assert distinctions 

Ipaceand f Space and Time, without proceeding to measurement 
Time. by units, must be ranked among comparative judgments, 
or, as these might otherwise be called, judgments of con- 
tinuous quality. It is not the business of Logic to analyse 

chap, ii.] Quality in Spatial Perception, 121 

the means by which the consciousness of extension or suc- 
cession is obtained. Logic only deals with the nature of 
such a consciousness, and not with its psychical genesis. 
But we cannot entertain a doubt that position in Time V 
or Space can only be indicated to consciousness by quali- 
tative marks that fall outside the content which is per- 
ceived as in Time and Space. Our inability, in many or 
most cases, to detect these marks by immediate observa- 
tion (I have never been able to analyse my seemingly 
direct perception of the quarter from which a sound comes), 
cannot, I think, outweigh the impossibility of showing 
other means by which the eye can judge distance, the ear 
direction, and the memory recal a series in its serial order, 
and no other. 

The only logical importance of this psychological analysis y 
lies in its confirmation of the idea, suggested by the facts of 
language and the very nature of quantity, that Space and 
Time must imply qualitative discrimination as an element 
of quantitative comparison. Nearer and further must be 
qualitatively distinct spatial perceptions, as red and redder 
are qualitatively distinct chromatic perceptions. Thus, the 
abstract totalities of Space and Time have their germ in 
comparisons effected by perception co-ordinate with the 
perception of continuous quality and of its differences. 

But the demonstrative judgments have forced upon our 
notice a further and peculiar distinction within space and time 
as continuous qualities, which is known in space as difference 
of direction, and in time as difference of past and future. 
' Nearer ' and ' further ' are different spatial perceptions ; 
and it is possible that 'this' and 'that' may be naturally 
equivalent to ' nearer ' and further,' as ' here ' and ' there ' 
must be, or must soon have become *. But besides ' this ' 
and ' that ' we have in space the distinction of ' that ' and 
' that,' ' there ' and ' there,' just as in time besides ' now ' and 
' then ' we have ' then ' and ' then ' a distinction which may 

1 Even if, prior to a spatial distinction recognised as such, there may have 
been a less defined distinction as between ' by me ' and ' not by me.' 

122 Quality and Comparison. [booki. 

apply to points equally removed in past and future, and 
therefore cannot be reduced to quantity, i. e. degree of 
remoteness. ' That ' and ' that,' ' there ' and ' there,' imply 
no difference of remoteness, nor indeed do ' this ' and ' that ' 
necessarily do so. 

All these may just as well mean on the right hand and 
on the left as nearer and further. They must indeed be 
comparable in distance, but it need not be distance that 
furnishes the distinction between them. With other qualities 
the case is different. There cannot be two different reds 
that match ; all reds that match, i. e. that are ' equal,' are 
the same. And if there can be two or more different 
musical sounds that have the same pitch, this is because the 
distinction between them is one of kind, not of simple 
quality, because, that is, they are composite perceptions 
which are estimated with reference to one element within 
them taken as dominant or essential. 

Thus it seems that (i) Space and Time appear in the 
germ as mere qualities whose continuity is displayed in the 
judgment of comparison like that of any other qualities. If 
apprehension of Space and Time really depends on ' local ' 
and ' temporal signs,' we must suppose that the peculiar 
definite externality which characterises extension could 
only appear by degrees, and that perception must have 
been transformed from perception of contents plus local 
signs, to perception of contents arrayed in extension by 
means of local signs, that the logical character of spatial 
perception, its continuity and homogeneous differences, 
must have been present from the first in any system of 
apprehension which could develope into our spatial world. 
The judgment of continuous quality admits of this. And 
(2) the distinctions which first present themselves within a 
given spatial or temporal perception are not simply and 
solely differences of quantity, though in time more so than 
in space, and in both capable of quantitative expression. 
They are more analogous to differences of kind. We must 
therefore take the spatial and temporal demonstratives, 

chap, ii.] Qualities as such are disparate. 123 

apart from explicit quantitative comparison in space and 
time, as in themselves comparative contents involving 
continuous quality. 

The divergence from the main progression of the judg- 
ment, by which space and time are erected into totalities 
having a special structure of their own and a peculiar mode 
of existence, must be taken as beginning with the resolution 
of a given ' now ' and ' here ' in the judgment of comparison. 
In this resolution we have the two grades, corresponding to 
distinctions of direction, or to the distinction of past and 
future, and to quantity respectively; first that in which 'this' 
and 'that' may be e.g. to left and right (not nearer and 
further), where the spatial comparison is implied rather than 
expressed, corresponding to the judgment, ' This is red, and 
that is green ;' and, secondly, that in which a true spatial com- 
parison is introduced into the content, as in ' This is nearer 
than that,' which is analogous to ' This is redder than that.' 

iii. Under the head of Comparison it is usual to treat of So-called 
like and different in kind, as co-ordinate with more and less. J^ tatlve 
But it is to be observed that such a co-ordination is not parison. 
accurate. Mere qualities, as such, are disparate, incom- ^ 

parable with each other. The judgment of quality pure 
and simple, as we have seen, excludes comparison. This 
is red, this is black, this is golden, this is sweet, this is sour. 
These are successive and isolated judgments of quality; and 
the semblance of comparison which they now bear is due 
exclusively to the advanced point of thought at which 
language places us to begin with. 

Comparison of degree, as we have seen, includes difference 
or elementary negation within the limits of a single quality, 
but the differences themselves, in regard to the aspect which 
makes them distinct, remain disparate or incomparable. 
In other words, every part of a quantitative whole is dis- 
tinguished by a peculiar quality as well as united with the 
rest by an identity of quality. Every shade of red, besides 
being a degree of red in general, is also a particular hue 
and produces a distinct impression. Every perception of 

124 Quality and Comparison. [booki. 

warmth is qualitatively peculiar, and often it is not without 
an effort that we can recognise the character in respect 
of which it can increase or decrease. Every inch in 
a yard measure, every cannon ball in a heap, is thus 
distinguished ; and if it were not so, the parts would have 
no stability and the quantitative whole would cease to 

We therefore are driven to conclude that quantitative 
comparison is not prima facie co-ordinate with qualitative, 
but rather stands in its place as the effect of comparison on 
quality \ which so far as comparable becomes quantity, and 
so far as incomparable furnishes the distinction of parts 
essential to the quantitative whole. It is with this latter 
aspect in which qualities are incomparable that qualitative 
comparison as such must be connected. It is thus, prima 
facie ', comparison of the incomparable. Any two shades 
of red, regarded as shades of red, are respectively 
more and less. But they must also be, as we have 
insisted, different reds, and if regarded simply thus are 
pronounced incomparable as a result of comparison. If 
we pass, as we can, by slow transitions, along the complete 
solar spectrum, comparing each colour with that which 
formed our starting-point, we shall arrive first at differences 
which may, and then at differences which must, be thus 
regarded. The difference between red and green, for 
instance, is not to ordinary perception a difference in the 
same quality; and if it can become measurable, can only 
become so by reference to an identical quality, such as 
brightness of illumination, which falls outside the pecu- 
liarities of red and green as such. 

I believe that it is futile to attempt the measurement of 
difference except in respect of a continuous quality. And 
the mere affirmation of difference, without the attempt to 
measure, appears to me absolutely devoid of meaning. 
The mere judgment, 'These two colours, these two 
sounds, or, these two perceptions (a colour and a sound), 
are different,' is an imperfect and unreal judgment, which 

chap. ii.] Quality and Kind. 125 

in this form, and apart from a meaning which I shall 
explain below, is as I believe to be found nowhere but in 
logical text-books. It may best be considered as an 
incomplete quantitative comparison, in which the parts are 
distinguished, but their place in a continuous whole has 
proved impossible to determine. In this sense, the mere 
judgment of difference would mark the initial effort of 
quantitative comparison. Such a relation is illustrated by 
the well-known fact that qualitative difference, e.g. between 
two musical notes, is perceptible before its quantitative 
nature (their relative pitch) is ascertained. Such a judg- 
ment of qualitative difference may be regarded as a first 
determination of quantity ; for its point is merely to deny 
identity of quality, and in matters of simple quality to be 
identical is to be equal and vice versa. In this sense the 
judgment of qualitative difference, such a judgment as we 
make when we see that two colours do not match, is an 
aspect of the initial stage of quantitative comparison. 

But another judgment of sameness or difference, which it 
is almost impossible to avoid confusing with the above, has 
its true place in classification and analogical inference, 
and, if explained as mere qualitative comparison, is an 
unreal fiction. Such judgments are : ' These two instru- 
ments are not in tune ' ; ' Gladstone and Chamberlain are 
very different men ' ; ' That victory is uncommonly like 
a defeat' ; 'The globe-flower is just like a hellebore, only 
it is yellow.' Here we are not speaking of an immediate 
qualitative identity and difference, but of essential and 
dominant qualities or rather attributes, in other words of 
differences valued by a presupposed standard or purpose. 
The idea of a standard involves the idea of kind, and kind 
goes beyond quality. Therefore, we come to a conclusion 
which I think frees us from much sham accuracy and 
pretended precision. The judgment of difference is never 
made apart from a standard of difference. The apparent 
exception, when such a judgment denies identity of quality, 
is simply the first step in quantitative comparison, and it is 


126 Quality and Comparison, [Booki. 

by quantitative comparison that precision must in such cases 
be obtained. But the class of judgments from which our 
later instances are drawn do not refer to identity of quality \ 
but identity of kind. They presuppose classification, and 
affirm difference or likeness with reference to this classifi- 
cation. All attempts therefore to introduce a quantitative 
estimate into these generic judgments of difference are 
founded on a confusion between judgments of quality and 
judgments of kind, on an attempt, that is, to reduce the 
latter to the former. This does not deny that the latter 
may imply the former in addition. 

It is a futile introduction of psychology into logic to 
speak of measuring difference by the difficulty or duration 
of a psychical transition ; the measure of the difference 
is what we mean by the difference, and what we mean 
by it depends on the series or classification within which 
we affirm it. Apart from such a standard the judg- 
ment of difference is nonsense ; it becomes like ' The soul 
is not square.' How idle to inform us that Gladstone and 
Chamberlain are different ! How superfluous to affirm 
that one plant is like another! Any assertion like these, if 
it is not referred to a ground of distinction, in these cases 
to political and botanical classifications respectively, is as 
destitute of content as a bare negation. The instance of two 
instruments pronounced out of tune with each other may 
seem not to be in place under this head, and to be a judgment 
of true qualitative comparison. I inserted it expressly to 
indicate the line of demarcation. Different colours are 
such as do not match, i.e. are not discernible in simple 
quality. But in comparing musical notes we have not to 
do with simple quality 1 , but with dominant quality *, i. e. 
kind. f A note' is identified by its pitch, and different 
notes are sounds differing in pitch. Therefore in pro- 
nouncing notes to be different we do not merely deny that 
they are indiscernible ; we deny more than this, we deny 

1 I use quality in the logical sense, in which it includes timbre (musical 
quality), pitch, and loudness. 

chap, ii.] Kind is Essential Quality. 127 

that they are indiscernible in their dominant quality , viz. 
their pitch. That the pitch is itself a quantitative attribute 
makes no difference ; for it is a quantitative attribute, which 
has become characteristic^ and therefore stands logically in 
the same position as any other basis of classification. 

In short, then, we must not confuse quality and kind. 
Kind is dominant or characteristic quality and involves 
a series of ideas which we have not yet discussed. And 
whereas comparison in respect of simple quality is prior to 
and absorbs itself in quantitative comparison, comparison 
in respect of kind is subsequent to quantity and involves 
other ideas. An isolated judgment of difference can have 
no meaning except as the first stage of quantitative com- 
parison, the negation of identity ( = this and that are 
unequal). The attempt to assign gradations to the mere 
judgment of difference rests on a confusion between quality 
and kind, each of which has in itself an adequate and 
objective principle of measurement independent of psychical 
transition, and in the case of kind, incapable of reduction to 


Measurement Quantity and Proportion. 

Measure- I x , MEASUREMENT is the equation of any whole, by com- 
ment and . . n . 
individu- panson, to a numerical aggregate of determinate parts. 

ahty. *phe p ar t s ma y be determinate through reference either 

outside or within the whole to be measured; but if the 

reference falls within it (as when we say a man's whole 

height is so many times the length of his head) the whole 

must be complex and contain subordinate systems. The 

reference may also take the shape of relations which are 

not purely quantitative (as a tone or semitone in music, 

apart from its physical cause, is simply a difference between 

two peculiar sounds) ; but in that case we are passing out 

of the region of pure measurement. Some reference, 

however, there must be in measurement beyond that to 

4 the simple whole which is to be measured. It is no 

measurement of a line to divide it into ioo or iooo equal 

parts. We must know what else they are parts of, besides 

being parts of the line to be measured. The length of a line 

is measured when it is equated to feet and inches to the 

length, that is, of some actual piece of metal agreed upon 

as a standard the pitch of a note is measured when we 

have determined its place in the scale or the number of 

vibrations per second that enter into it ; the specific gravity 

of a substance is measured when we have stated the ratio 

of its weight to that of an equal volume of distilled water at 

a certain temperature. Here a verbal difficulty may be 

cleared away. If the weight of the substance before us is 

twelve times that of water, our definition of measurement 

applies straightforwardly. We equate the whole substance 

in respect of its weight to a numerical aggregate of twelve 

parts, each of which is determined by equation to a known 

chap, in.] Measurement and Comparison. 129 

volume of water 1 . But if the substance is ^ of the 
weight of water, we seem not to be breaking up the 
whole which is being measured into an aggregate of parts, 
but to be representing it as a part within another aggre- 
gate. This is a mere matter of practical convenience. 
The equation of a whole to a numerical aggregate is as 
much involved in the expression ft (a twelfth part), as in 
the expression 'twelve times.' In measuring, we bring 
two terms into precise equation, and the entire relation of 
whole and part is involved in each. The numbers in which 
the same part enters into two or more wholes are in every 
case the organon of measurement. 

i. Measurement is to begin with Simple Measurement, Simple 
resulting in pure Quantity. mtnt^ 

Simple Measurement consists in judging of a perceived Quantity, 
object that it is a whole containing a certain number (one 
or more) of a determinate unit. Measurement is thus a 
development of comparison, which is the first revelation of 
the unit, or equal part the result of successful equation 
within continuous quality. Simple qualitative identity, for 
instance, such as that of colours which match, may be set 
down to comparison or to measurement according as it is 
or is not ideally referred to a scale of degrees. In pure 
qualitative identification we have sometimes no idea of 
possible degrees, and such identification must be regarded 
as the earliest germ at once of measurement and of com- 
parison. Thus ' The taste of this is the same as the taste V 
of that ' is mere identification or comparison if it only 
means that the tastes of the two things are indiscernible, 
but is measurement if we are considering whether the 
one taste is sweeter than the other. We have seen that 

1 Practically of course we do not heap up volumes of water in one scale till 
they balance a substance in the other scale. The process employed is equivalent 
to weighing first the substance, and then the water which it displaces, against 
known standard weights, and taking the two results as a ratio ; i. e. by help of 
the balance we state the two things to be compared in terms of an aggregate 
of already known and determinate parts ; one thing will = 12 oz. and the other 
1 oz. 

VOL. I. K 

130 Quantity and Proportion. [booki. 

qualitative identification is only the germ of quantitative 
comparison, and that the two are not co-ordinate l . 

How is the unit fixed ? It is fixed, as we have seen, by- 
equation or identification of it as the same throughout the 
various wholes or aggregates into which it enters as a part. 
This process of equation tends to repeat itself ad infinitum. 
Pure quantity is an essentially relative attribute. Hence 
in Simple Measurement the paradox of knowledge takes 
an extreme form, for every measurement presupposes and 
provokes others ad infinitum. The tables of weights and 
measures of our arithmetic books are enough to illustrate 
this. They are long lists of equation after equation, by 
means of which all objects that are measured or weighed 
are ultimately equated with some single portion of matter 
or relation in nature 2 , arbitrarily selected as a basis of the 
division and multiplication that facilitate comparison. The 
substitution of a determinate physical motion supposed to 
be constant for a particular portion of matter makes no 
change of principle so long as it is taken qua a term in 
a fixed ratio or mere ratio, and not qua a term in a 
>/ generalised ratio or proportion. But in fact the two ideas 

are at bottom inseparable. Everything fixed is qua fixed, 
potentially generalised. The wave-length of what is a 
particular red to a normal eye does not vary (so far as I 
know), but this is so to speak an accident ; and if we take 
in non-normal eyes, all that is certain is that this wave- 
length preserves its place in the colour-series above some 
wave-lengths and below others. Its fixity for red judged 
by the healthy eye has however caused it to be suggested 
for an unit of length. Weight the relation of a portion 
of matter said to weigh 1 lb. to all other portions of 

1 P . 123 ff. 

2 Such as a fraction of the earth's circumference. But any such relation is 
likely to be variously determined at different times, while it is not convenient 
to alter the basis of a system of measures. I believe that practically all systems 
of measures depend upon the actual material standard, which as a mere piece 
of metal, not capable of being tested by any general relation in nature, must be 
reckoned as a purely arbitrary standard. 

chap, in.] Generalised Measurement. 131 

matter in respect of their gravity becomes a generalised 
relation or proportion the moment we consider distance from 
the earth's centre. * 1 lb. at earth's surface : % lbs. at earth's 
surface : : 1 lb. five miles up : 2 lbs. five miles up.' When 
a thing is described generically by the number of its own 
parts this is more obvious, for the ratio is then ipso facto 
generalised by the mere recurrence of individual things. 
But simple measurement of perceived objects gives simple 
ratios expressed in singular judgments with external refer- 
ence. As the judgment becomes general the ratio becomes 
first formally proportional, because the ratio is generalised 
as against instances in which it occurs, and then really 
proportional, because this generalisation comes to apply to 
cases in which the corresponding terms are different mag- 
nitudes. The ratio between measures 1 is formally propor- 
tional ; that between weights, explained as above, is really 

ii. Thus measurement necessarily becomes complex, Complex 
ideal, or mediate; i.e. in short generalised. In this aspect measure- 
it first appears within the singular judgment, and then ment - 
breaks loose from it. tion. 

Every relation established by measurement is a ratio, or 
relation between magnitudes ; and as incommensurable 
magnitudes are for logic a contradiction in terms, every 
ratio can be expressed in so far as it is a true ratio 
(in so* far as its terms are magnitudes) by a relation 
between two numbers. Number refers the relation to an 
abstract whole of quantity, and therefore determines the 
identity of the relation by its place in a self-identical 
articulate system. But the effect of such expression is 
to generalise, while the results of simple measurement 
can warrant no generalisation, and therefore are not spoken 
of as a ratio, and often not reduced to their simplest 
numerical expression. Nothing would be gained by saying 

1 By ultimate refinement, this too is really proportional. Suppose all 
measurable things to expand and contract preserving their ratios, we could 
never know it. Given a foot-rule, we could still construct a yard-measure, 
however the absolute length of the foot-rule might vary. 

K % 

132 Quantity and Proportion. [Booki. 

that a given plant 5 ft. high had a height which was to 1 ft. 
as 5 : 1, nor by judging that this piece of lead is to this 
piece of gold in weight as 11 to 19. The ratios so affirmed 
would still be destitute of general significance, would be 
mere facts, alleged of a particular reality present in per- 
ception, and would therefore gain nothing, but might lose 
their truth, by abstract expression. 

But thought always tends to coherence and necessity, 
and we cannot even employ a determinate idea to assist us 
in pointing out an object of perception without creating 
the impression that the ideal content which we use will 
be characteristically connected with the content of our 
predication. When this occurs in the judgment of mea- 
surement, ratio passes into proportion ; that is to say, the 
ratio enunciated as true of the particular given subject 
becomes a universal rule applicable to all variations com- 
patible with the determinate idea which conditions the 
subject. Such measurement is complex, because the unit 
on which it is based is no longer single and fixed, but 
variable in absolute magnitude, though determined by a 
condition. It is ideal, because no longer a mere fact of 
sense-perception, but enunciated as flowing from a content 
intellectually defined. It is mediate, because the reference 
to reality which constitutes this as every judgment, is not 
direct, but has to pass through a condition before it can 
attach to reality. 

Therefore if we take one of the above simple measure- 
ments, and even without removing the demonstrative ' this,' 
insert a determinate condition into the content, we shall 
find that the whole affirmation is greatly modified in its 
nature. Let us judge that 'This piece of lead and this 
piece of gold, being of the same volume, are found to be in 
weight as 11 : 19.' Then we at least suggest the erection 
of the ratio 11:19 into a law of proportion : 'The weights 
of equal volumes of lead and of gold are as 11 to 19.' 

So again, we may have simply counted the leaves on 
a plant-stem, going round the stem in the same direction, 

Chap, in.] Charactei'istic Ratio. 133 

till we find a leaf immediately over or under that from 
which we began. If we do not know that these ratios are 
characteristic, or if we suspect the plant to have been 
injured so as to make its ratio undiscoverable, we may 
simply judge, 'On this plant I find five leaves in going 
twice round the axis.' Whereas if we insert the name of 
the plant or tree, and use an abbreviated expression for the 
ratio of divergence, we at least suggest the idea of a cha- 
racteristic law of the leaf spiral. 'This oak shows a diver- 
gence of I ' (i. e. the sixth leaf is directly over the first, and 
in counting from 1 to 6 you have gone twice round the 
stem). It is obvious that here generalisation and cha- 
racteristic attribution have begun. Granting that we have 
not yet any assertion about the genus oak, or even about 
the species in question, for the ' This ' hinders such an 
interpretation, yet we unquestionably are awakening to the 
expectation that the tree before us will present the ratio in 
question in all its different parts and from time to time, and 
to the problem whether and how far we may drop the 
' This ' which indicates particularity. When the ' This ' is 
dropped the judgment ceases to be singular, unless it is 
attached to a proper or in some way individual name. 
Whether and how far, failing these refuges, it ceases to be 
categorical and becomes hypothetical, or how far indi- 
viduality continues or even revives after the loss of particu- 
larity, as a factor in the evolution of thought, is a question 
which will frequently occupy us in the sequel. 

Characteristic ratio, or proportion, may refer to standards 
external to the whole which it qualifies, or to relations 
within that whole. In the former case the qualitative 
quantity remains subject to relativity and eked out by 
equations ad infinitum^ hardly less than in the case of 
simple measurement. 

In any table of specific gravities, for instance, we have 
a number of substances each severally characterised by the 
ratio of its density to that of distilled water at a temperature 
of about 39. i Fahrenheit. Now in the first place, each of 

134 Quantity and Proportion. [bookt. 

these several ratios may obviously be regarded as a propor- 
tion in so far as it applies without variation to any volume 
of the same substance, in the sense that the weight of any 
volume of any substance is to the weight of the same volume 
of water 1 in the ratio of the specific gravity of the sub- 
stance. Proportion is defined as ' equality of ratios ' ; and 
equality of ratios obviously is identity of the ratio, and exists 
between every ratio and all cases in which it applies. 

But in the second place, although in these cases we have 
proportion, yet we have also relativity ad infinitum. Select 
the specific gravity of some one body, and suppose that of all 
the rest except water itself to be erased from knowledge ; 
the significance of our one fragment of information would 
then be all but gone, were it not for the accessory idea, 
which we cannot now get rid of, that the rest could easily 
be recovered. Apart from this accessory idea, the sup-^ 
position makes it plain that the ratio between the density 
of silver or flint glass and that of water is not sought out as 
valuable per se, but is valued as a means of equation with 
all measurable densities. In such instances as these we 
have the first grade of characteristic quantity or proportion, 
still subject to an external relativity which extends into an 
infinite series. 

Now though this relativity never disappears as an aspect 
of human knowledge, yet characteristic quantity can assume 
a more self-sufficing position than that which has just been 
described. Instead of developing the this and that of the 
comparative judgment into separate units connected only 
by an abstract identity of quality, we may consider them as 
structural elements within a concrete whole. As before, we 
shall find ourselves at first in the stage of simple measure- 
ment and pure quantity. But the tendency to advance to 
proportion is in cases of this type much more pronounced, 

1 I omit for the sake of brevity in this and parallel cases to repeat in every 
sentence the precise determinations by which the standard unit is made a 
standard. But it is all-important to remember that there are such determina- 
tions, and that they in turn need re- determination ad infinitum. There is no 
ultimate unit. 

chap, in.] Proportion and Individuality. 135 

because the parts of an individual whole are more likely to 
vary in connected ways and therefore lend themselves to 
proportion, than the elements of wholes external to one 
another. Still we begin with pure quantity. ' This plant 
has petals exceeding the calyx segments/ or ' has radical 
leaves half the height of the stem,' or 'has twenty-one 
carpels and forty-two stamens/ or, as we said above, has 
a divergence of f between its stem-leaves.' In the first 
instance such judgments as these are mere judgments of 
perception, or at the outside of direct historical fact, and the 
ratio which forms the content of predication is therefore 
not a proportion, because it has no extent of application. 
In proportion, the ratio is to the cases of the ratio as Inten- 
sion to Extension. 

But the moment thought has seized a designative idea, it 
is committed and must go wherever the idea carries it, in 
despite of the demonstrative ' this.' And the moment that 
any such internal ratio as those which I have suggested is 
taken to be characteristic, i. e. to be involved in the desig- 
native idea, it becomes a proportion, i. e. a law of structure 
which holds in spite of varieties of size, shape, and number, 
although, at least in natural objects, always subject to limits 
which as regards the proportion itself are arbitrary and 

Proportion is the simplest expression of individuality. 
All intelligent recognition of individual objects depends 
either on proportion or on some principle which involves 
proportion. It is in this that the truth lies of the well- 
known Pythagorean doctrine that all things are embodi- 
ments of number. All things have aspects and effects which 
find generalised expression in number. Shorten a snipe's 
beak, take one from the divisions of the horse-chestnut leaf, 
or misplace the accent (a variation of loudness and duration) 
in an English word, and recognition falters or fails. Even 
a human character or an artistic inspiration, though not in 
itself susceptible of numerical expression, leaves traces in 
all its acts and products of an individuality that takes shape 

136 Quantity and Proportion. [booki. 

in proportion or qualitative quantity. An exhaustive statis- 
tical treatment of a man's life in all its tangible aspects would 
give, by the graphical method, not indeed his character, but 
a set of proportions penetratingly significant of his character. 

It may seem indeed that in common hurried thought 
recognition simply attaches to some pre-eminent quality, 
a bright colour, a marked outline, a peculiar movement ; 
and that such elements as these, without extension into 
proportional systems, furnish the practical meaning of 
words in ordinary life. But in the first place, this is per- 
haps a superficial analysis of perception. I very strongly 
doubt if the element of proportion, both external as in 
size compared with surroundings, and internal as in shape, 
symmetry, or harmony of sound or colour, is ever absent 
in a recognitive perception of an individual thing. A really 
abstract quality would hardly mean anything ; we should 
be able to place it nowhere in our world ; and if we even 
recognised its degree of intensity, that would at once con- 
stitute a quantitative element. It has indeed been observed 
that a familiar scent (one of the least articulate of qualities) 
has a notable power of stirring associated memories. But 
this seems so noteworthy just because the scent does not 
recall any individual thing, but rather brings back a general 
state of feeling connected perhaps with entire scenes and 
incidents, but especially with emotions. 

And in the second place, if an abstract or mere quality 
were used designatively in judgment, it would not grasp 
or enter into the nature of a real individual ; it would 
simply be a falling back towards the demonstrative affir- 
mation with its ' This,' which may on occasion be eked out 
by any element that draws attention. 

But all ordinary recognition of individuals undoubtedly 
depends on the judgment of proportion. We cannot indeed 
tell the specific gravity of a metal by the mere sense of 
pressure or of resistance, but we know how a sovereign 
ought to feel when we lift it on the palm of the hand ; and 
though we may call this effect on the hand a quality, it is 

chap, in.] Internal and External Proportion. 137 

plainly a quality pervading differences and so quantitative, 
and moreover taken as characteristic and so proportional. 
Consider once more the effect of altering an accent in 
English (I do not speak of languages in which accent 
depends on pitch) as exemplified in the change of ' conquer' 
into ' concur' by transferring the stress from the first to the 
second syllable, or the utter unrecognisability of such a 
term as ' sleeping-car' when pronounced with a heavy stress 
on the second syllable 1 , and a light stress on the first. Here 
it is the internal proportion that is modified, with the result 
of destroying the peculiar rhythm by which in a great 
degree the ear instantaneously recognises a word. The </ 
more marked an individuality is the more it depends on 
internal proportion. Every instrument fitted for a purpose 
has internal proportions dictated by its purpose ; a knife is 
sharp at the edge and blunt at the back ; the thickness of 
the blade in its transverse section depends on the require- 
ment of strength on the one hand and on that of dividing 
without displacement on the other, and these requirements 
together dictate a certain set of proportions characteristic 
of a blade suited for some particular purpose. The length 
of the blade compared with its width depends on such 
another set, and its temper on a third. All of these being 
on the one hand relative to each other and on the other hand 
relative to a purpose are internal proportions subject to limits 
prescribed by external proportions. It is by acquaintance 
with the perceptible character impressed by such proportions 
as these that we readily pronounce on the use of objects 
made by the hand of man, and that we detect, somewhat less 
readily, the actual purpose served by adaptations in the or- 
ganic world. Such attributes as are expressed in these pro- 
portions form, for perception, the content of individualities. 

It follows from these considerations that the question of 
individuality in contents the main attributes of which arise 
from external proportions is not an easy one. Such are 

1 The author once heard the words thus mauled at Calais, and could not 
imagine what was being said, though no elements of the sound were omitted. 

138 Quantity and Proportion. [booki. 

nearly all inorganic substances, except where adapted to 
a purpose by man. External proportions per se produce 
no effect of individual unity, and though it is true that all 
substances occur in particular fragments which have de- 
finite characteristic forms, yet the ratios which would ex- 
press these forms are not absolutely typical or essential 
(though perhaps all substances prefer some shapes to 
others, and have typical fractures, &c), nor do the par- 
ticular masses of substances or volumes of gases demand or 
receive individual names. Professor Jevons has called atten- 
tion to this curious fact, which goes deep into the nature of 
individuality. Below the level of organic form, or form 
given by human interference, what do we mean by a thing} 
Of course we may take a lump of metal or an ounce of 
water, a handful of sand or a jarful of chlorine, and speak of 
it as- a thing ; but we shall be puzzled to find any name that 
recognises its separate identity as ' lion ' or ' spade' or ' house ' 
recognise that of the contents that form their meaning. Is 
gold a class-name, say a specific name, and are the actual 
pieces of gold individuals under it ? This does not seem to 
be right ; a class-name is true, without further determination, 
of the individuals under it. ' This is a lion,' ' This is a spade,' 
&c. But you cannot say ' This is a gold ' : you can only say 
'this is gold,' where 'gold' almost='made of gold,' i.e. is 
adjectival, and has no plural, or if it has one, uses it for 
different kinds, not for different pieces, of gold. 

It is enough at present to call attention to this difficulty 
as illustrating the place of structure in individuality. It 
should be noticed that a structure however complex which 
repeats itself homogeneously throughout all atoms of a cer- 
tain substance tends to confer individuality, if at all, on the 
minute units in which the complex structure exists, but 
neither on the substance as such nor on its larger frag- 
ments ; the supposed minute structure is not the structure 
of it or of them, but only a structure repeated within it or 
them. A heap of corn is, qua heap, no more organic than 
a heap of sand. But it may be for instance that, in virtue of a 

chap, in.] Disparate Qualities how combined? 139 

common structure, all the iron that anywhere exists is united 
by reciprocal reaction in a common magnetic world ; if so, 
it is then up to a certain point single and individual. The 
further consideration of this difficult subject belongs to the 
discussion of the Individual and Generic judgment. 

iii. The relation of Quantity to Quality results at this Qualitative 
point in a further problem. Assuming that a thing which jndivi- f 
has marked individuality has always a number of pervading duals, 
qualities, each of which contains gradations and a distribu- 
tion expressible by a ratio or proportion, what are we to 
say of the interconnection of these various systems of pro- 
portion with one another? Is it necessary that there should 
be a general proportion of proportions which, whether our 
actual apprehension of it be rough or exact, must be taken 
as capable of expressing the various systems of attributes as 
gradations within one and the same totality ? Is there any 
sense in talking of the proportion not only of length to 
length and of colour to colour, but of length to colour ; or 
of the proportion not only between rhythm and rhythm or 
pitch and pitch in a melody, but between rhythm and pitch as 
elements of the musical effect ? 

The view which we took above of the effect of comparison 
upon quality forces this suggestion upon us. If in other </ 

words, a single qualitative effect pervades any and every 
totality which we apprehend, and if within such a quality 
there are parts perceived as differences of it, then these 
differences must in respect of that quality be regarded as 
gradations. It is not necessary to press this conception 
home at present. It is possible that there may be indi- 
viduals whose unity lies in an idea only and not also in 
a quality, and that an idea may hold together without 
crushing them into gradations, antitheses which a quality 
could only admit as quantitative. But it is worth while to 
bear in mind two things. In the first place, the initial judg- 
ment of mere difference, ' Colour is not form,' may always 
be regarded as an equation of one term to zero of another. 
And in the second place, there may be a quality of ' effect/ 

140 Quantity and Proportion. [booki. 

or secondary quality, within which even form and colour or 
pitch and rhythm may take their place as degrees, just as 
the repetition of analogous though different forms in a picture 
or design gives the impression of a pervading character 
which is more and less intense in different parts of the 
work. Take for instance a picture about which there is 
a question whether Turner painted it, or a song which is 
ascribed without certainty to Shakespeare. In such cases 
we point to this and that characteristic as more or less 
Turneresque or Shakespearean ; and the elements so desig- 
nated need not be in actual sensuous quality comparable 
with each other. It might even be suggested that the 
exhibition of such a pervading quality was a condition of 
aesthetic though not necessarily of actual individuality ; 
a suggestion which would raise the fundamental problem 
whether all actual individuality has, for those who have eyes 
to see, a thorough characteristic unity. It would seem not 
improbable that true individuality is attained by actual 
individuals in very different degrees. 
Change iv. In explaining the apprehension of individual things, 

Preference wnicn * nave set down to the sense of proportion, it is usual 
tolndivi- to lay stress on the fact of change, including motion. 
Change in time and place is no doubt a primary instrument 
in revealing the fact of individual existence. The move- 
able and modifiable Thing proclaims itself unmistakeably as 
distinct and permanent. Nevertheless, for logical purposes 
change is only a case of difference or negation ; or if in fact 
the two are coextensive, yet change is not the essence of all 
difference. It may be that every apprehension of difference 
requires lapse of time, but this is only because our activity 
is in succession, and does not mean that the differences 
themselves must be (though they may be) successive. 

What the whole matter comes to is this. Difference is 
the principle which when generalised is known as Negation ; 
in as far as contents merely differ, they are merely not each 
other. Every continuous quality includes negative determi- 
nation, i. e. differences, elements which are not each other. 


chap, iii.] Change and Difference. 141 

Among other continuous qualities, duration and extension 
characterise a large part 1 of the world of sense-perception, 
and duration characterises in one aspect everything that 
comes before the human intelligence. It is not, therefore, 
surprising, that not only the parts or elements of individuals, 
but the individuals themselves as parts or elements of our 
perceived world, should bear a negative relation to each 
other and to themselves in time, in space, or in time and 
space together. 

Now if we contrast change and motion on the one hand 
with mere perceived difference on the other, as influences 
bearing upon the apprehension of individuality, the distinc- 
tion between the two cases amounts simply to this, that in 
the latter we have a single set of differences, which can go 
but a short way, as a rule, to exhaust any identity, while in 
the former we have at once a summary of innumerable 
differences or negative relations. These differences, in virtue 
not of their mere spatial or temporal distinctness, but of their 
positive content, are read off in judgments which may 2 
coalesce into one or may be distinguished into several 
determinations of the individual. These judgments may 
have a negative or positive form, but must always express 
a partly negative element of apprehension, viz. that ' what is 
not B is not A.' 

When we see a moving animal against a variously coloured 
background, different elements of its outline and colouring 
are successively thrown into relief by successive contrasts, 
and perception traces its form with increasing completeness 
by the negations which these contrasts furnish, i. e. by the 
correction which is effected when a line or colour, which 
the moment before ran into the background, is sharply 
defined by a change of contrast. The perceptive judgment 
resulting from this change will take the shape ' That (the 

1 I cannot think that sonorous bodies appear to be clothed with sound as 
luminous bodies are with colour. To me sound is an unextended perception, 
though referred to a cause in space. 

2 See the general theory of judgment in time, chap. i. above. 

142 Quantity and Proportion. [booki. 

dubious border of colour) was not B (a particular part of the 
animal's outline) and therefore is not A (does not belong to 
the animal).' More elaborate interpretations than this may 
of course attach themselves to the motion of a separate 
material thing ; thus, for instance, that which moves all 
together must in all probability have mechanical cohesion, 
for it is unlikely that in presence of varying friction at its dif- 
ferent points the parts of a moving appearance should keep 
together apart from such a condition. But cohesion is for our 
present purpose merely a definite content assigned to unity, 
and the negative relation of the moving thing to what does 
not partake of its cohesion is established by just the same 
logical process as its relation to that which does not partake 
of its distinctive shape or colour. Change in time without 
motion has the same effect ; nothing is more readily detached 
from- its background and apprehended as individual than an 
object whose transformations take place before our eyes in 
surroundings which do not share them. The judgment or 
judgments 1 'What is not a l9 a 2 , a 3 , &c. is not A' seems to 
form itself in such a case almost without an effort of mind. 
We shall be told indeed that ' What is not a v a 2 , &c. is not 
A' is a mere inference from ' A is a v a 2 , &c.' This objection 
would raise questions which cannot be dealt with till we treat of 
negative and of inductive inference. Here we need only insist 
that however we may elect to describe the process of the nega- 
tive instance, it is easily seen to be the most effective instru- 
ment of definition. When we inject a system of vessels with 
coloured fluid, in order to observe them under the micro- 
scope, it is not the particular colour, red or blue, that we 
look for, but the contrast between the artificial colour and 
the dull grey or yellow of the background. Even granting 
that we start from ' The vessels which are to be traced (A) 
are the red lines (a lt a 2 , &c.),' still this judgment cannot 
have scientific precision apart from the determination of the 
detailed not a v not a 2 , &c. ; and when the not-^'s assume 
a positive character, the negation ceases to be an inference 

1 See the account of judgment as an act in time, p. 85 ff. 

Chap, in.] Measurement leads to Necessity. 143 

from the affirmation A is a. And change is an infinite suc- 
cession of such contrasts, that gives every element of the com- 
plex individual before perception its chance of being sharply 
defined, and by successive negations defines each of them 
both against its own permanent elements and against the 
background. Instead of the simple change of colour by in- 
jection, let us think of the effect produced by rotating the 
polariser or analyser while observing an object that modifies 
polarised light. The successive but gradual changes of colour, 
illumination, and background which are thus obtained bring 
out the details of a structure as clearly as if we could handle 
it and move it freely in space. Change and motion merely do 
for a single individual identity what a comparison of instances 
does for an abstract identity. That is to say, they show 
through what contrasts the individual can pass, to what 
negations it can be subjected whether within its content, or 
between its content and the background from which it is 
distinguished, without losing characteristic identity. Change 
and motion have their logical value simply as embodiments 
of difference. 

v. In the Judgment of Measurement we find ourselves Abstrac- 
face to face with the element of abstraction and necessity, Necessity 
the medium in which exact science moves, and the occasion 
of the most fundamental crux for logic as for ethics. We 
are no longer, as in the Judgment of Quality, simply as- 
cribing the meaning of an idea to an unspecified reality 
given in perception. We are indeed, as always in judgment, 
defining the reality which perception presents to us ; but 
we find that in trying to define any special feature or 
element within it, we are under constraint, not merely as 
always from the pressure of perception, but from the ina- 
bility to select and connect at pleasure within the presented 
content. Judgment so far as it escapes from the dis- 
tractions of mere association proceeds in grooves or along 
threads which are always leading it across and out of the 
picture. It cannot, in the present stage at all events, simply 
characterise a given identity by differences related to it and 

144 Quantity and Proportion. [Booki. 

to nothing else. Such differences, as we have seen, would 
have no stability, and could characterise nothing ; although 
the more highly organised and individual the identity the 
more capable it is of prescribing a necessity to subordinate 
wholes which appear as differences within it. The course 
of judgment within the present whole of perception is deter- 
mined by connections which refer beyond that accidental 
whole, to other more comprehensive totalities, and ulti- 
mately, in every case, to the system of the known world. 
The connections thus prescribed between part and part 
within some systematic whole are necessary connections, 
and judgment, in so far as it is controlled by them, is ab- 
stract or hypothetical judgment. 
j But the appearance of this element in the judgment of 

perception makes it simply self-contradictory. The specifi- 
cation of a subject by means of an idea, which is only meant 
to point out a feature in present reality, brings the judgment 
into a groove of necessity, and all but makes its affirmation 
J conditional. A speaker who has affirmed that ' This exe- 

crable ruffian should be hung' will probably, if convinced 
that the man is not a ruffian at all, consider that the non- 
existence of the condition precludes the application of the 
judgment; i.e. in spite of the 'this,' he will maintain that 
his judgment was essentially conditional. We shall not find 
it easy to decide whether the idea in question was really 
a condition or a predicated content. In the latter case the 
judgment is falsified by the non-existence of the fact in- 
dicated in the subject, in the former it is not. There can 
be little doubt that we must follow the analogy of ' this/ 
'here' and 'now,' by treating ideas, which designate the 
subject, as presupposed rather than affirmed ; but seeing 
that in this case the idea which forms the presupposition is 
such as may or may not be realised, and yet is welded to- 
gether with a presupposition the ' this ' which cannot but 
be realised, there is an inevitable ambiguity in the judgment, 
the ambiguity between absolute and conditional assertion. 
Absolute vi. In logic as in ethics, Individuality or Absoluteness is at 

Chap, in.] Relativity and Explanation, 145 

first sight opposed to Necessity or Relativity. That which and Con- 
is individual or absolute claims to be self-sufficing ; that is Affirma- 
to say, to be an Identity which determines and is deter- tion - 
mined by its own differences, but is not dependent on 
anything outside itself. Every content partakes of this 
character in so far, but in so far only, as it has a unity or 
an interest for its own sake or in itself. A material ' thing,' 
an organism, a work of fine art, possesses such unity in a 
degree that forces its individuality upon perception and en- 
sures it universal recognition in language. But every content 
without exception that is exhibited in judgment has such 
unity or interest in some aspect or to some degree. Even 
the abstract idea that qualifies c this ' in a perceptive judg- 
ment such as ' This cold is intolerable ' is taken as the key 
to the interest of a presentation, as a predominant feature 
that arrests attention in our momentary surroundings. That 
the distinctive character which makes the unity of the pre- 
sentation is abstract and indeterminate follows merely from 
the judging function being in a rudimentary stage to which 
a concrete synthesis is still unattainable. 

On the other hand, every judgment may also be regarded 
under an aspect of relativity or necessity. In so far as a 
content is necessary it is not self-sufficing, but is a conse- 
quence of something else, and in so far as it is relative it 
fails to explain itself, and refers to something else for ex- 
planation. Every content, every identity in human know- 
ledge is on one side wholly of this character. How the two 
sides, the absoluteness and relativity of the objects of 
knowledge, can coexist without interfering may be consi- 
dered if we please, though in my judgment erroneously, as 
a desperate problem. But that they do coexist we may 
convince ourselves by the evolutional history of any flower, 
by the analysis of any ornamental design, by the study, in 
its genesis and with a view to the influences that conditioned 
it, of any human mind. And, in one sense, necessity is more 
universal than what I call absoluteness, or if I may coin a 
phrase significant of the sense in which I speak of absolute- 

VOL. I. L 

146 Quantity and Proportion. [booki. 

ness, morphological unity. Morphological Unity has de- 
- grees, but relativity or necessity has none. The only escape 
from relativity is in the exhaustion of relations. If, for 
instance, we can intelligibly speak of the universe as a whole, 
we must take it, I presume, as the totality of relations, and 
therefore as bearing no relation to anything outside itself. 
But this speculation is unprofitable, because what is out of 
relation is out of knowledge ; or it has at most a negative 
value as against doctrines which extend the relativity which 
holds within the totality of relations to the ideal totality of 
relations itself, and so discuss its origin or the possibility of 
it not having been. This is futile, from the very nature of 
explanation. All explanation is within the universe, not of 
it. Therefore every content that designates a subject invites 
consideration as an antecedent in necessity in a judgment 
'if a is, then b is,' while it is not every content that has 
morphological unity and so is given as a whole in each and 
all of its differences. And only such a content as this is 
adequate to reality, or can stand, without special symbols 
of reference, for an individual reality. What is not indi- 
vidual cannot as a whole be real. 

The above considerations were touched upon in chap. I. 
in explaining the pregnant distinction between Categorical 
and Hypothetical judging, and are to govern, as was there 
indicated, the application of that distinction in the remainder 
of the present Book. We start from the principle that all 
judgment whatever is an attempt to make explicit the nature 
of Reality, and is directly or indirectly attached to the 
-reality which is presented through perception. The ulti- 
mate subject of all Judgment is the Real, and any idea which 
appears as designating or even as in lieu of the subject of 
judgment must be taken as simply indicating or calling 
attention to some aspect of the real world. That is to say, 
such an idea must be taken as morphologically correspond- 
ing to the ' this,' ' here,' or ' now ' in the demonstrative 
judgment, to the unnamed direction of perception in the 
pure judgment of quality, or to the designative ideal con- 

chap, in.] Individuality and Reality. 147 

tent which expands the ' this ' or * here ' in the elementary 
judgment of measurement. It follows from this that in 
every judgment the immediate subject is prima facie taken 
to be real, and therefore every judgment is prima facie 
taken to be categorical. This does not mean that in the 
strict sense it asserts real existence of the subject, for its 
real existence is presupposed \ but rather that it defines the 
reality of a real existence presupposed as subject. 

But this prima facie semblance of the judgment must be 
qualified. The explicit content which designates the real 
subject may be inadequate to the nature of reality. In 
1 this red thing,' ' this metal/ even ' this man,' the explicit 
contents ' red/ ' metal,' ' man ' are typical and general, not 
single and individual ; and still more is this the case if we 
think of such judgments as ' Red is a colour,' Metal is lus- 
trous,' ' Man is mortal.' These contents stand for imperfect 
and incomplete realities ; realities that could only be com- 
pleted in an infinite series of time and space. The difficulty is 
not that they go beyond present perception and beyond our 
knowledge. Caesar is not in present perception and we do 
not know all that he did, yet in 'Caesar crossed the Rubicon' 
no one doubts that Caesar is a reality. Caesar is an indi- 
vidual, and his entire identity is present in his every act and 
attribute. Man is no doubt a definite concept, but its 
instances or manifestations have not prima facie individual 
identity one with another. The centre of morphological 
unity is in each separate human being, not in the idea of 
the race as such. The concept, as we commonly think it, is 
an abstract idea, and the reality that corresponds to it is a 
series of individuals, which not merely is not yet actual as 
a whole, but is not in our predication treated as an actual 
whole. The reciprocal relations which bind together say the 
English nation or the Roman Empire into a historical indi- 
vidual may be present also more or less in the case of 
humanity, but when we say ' Man is mortal ' this is not the 
light in which we look at the Subject ; we are speaking of 

1 See last section. 
L % 

148 Quantity and Proportion. [booki. 

individual men whom we designate by help of the concept 
man, not of humanity or mankind as such, for which it might 
be maintained that morphological unity is possible. No 
doubt however, if we push the matter home, even the predi- 
cate mortality is affirmed of all individual men in virtue of 
a oneness of nature running through them all ; and therefore 
we must, as I have said, take the individual unity to be a mat- 
ter of degree, and to be wholly absent in no content that can 
be presented to thought as designating a subject of judgment. 

When, in view of cases like these, we qualify the principle 
laid down above that in every judgment the subject is taken 
as real, we must do so by the emendation, ' The subject is 
taken as possessed of that kind of reality of which it is 
capable, subject to any alteration which the predicated 
content may declare in such reality.' The first part of this 
sentence provides for judgments introduced by abstract 
ideas and not referred to actual individuals, the second for 
all kinds of judgments which formally affect reality and 
which are alleged * as proofs that content and reality cannot 
depend upon one another. First among these come the 
Negative Judgment which sets up an aspect of Reality in 
order to demolish it, and then all such peculiar cases as 
'The chimera is a fiction,' 'Nothing is here,' 'A wise knave 
is a contradiction in terms.' 

The view to which I have just alluded might raise an 
objection at this point, which I will only mention in this 
place, as the real answer to it, if any, can only be found 
in the whole conception of the judgment which we have 
adopted. 'Whether an idea stands for a reality or not 
does not depend on its content, but on that content being 
recognised as somehow and at some distance or other 
belonging to the world continuous in quality with the 
object of present perception i. e. to the actual world.' 
My answer to this would be that I have accepted this 
identification in quality as the abstract logical or rather as 
the psychological condition of all judgment ; but that this 

1 Bradley's Principles of Logic, p. 14. 

Chap, in.] Necessity in Judgment, 149 

identification is empty apart from the specific kind and 
degree of reality assumed or alleged, and this, as it appears 
to me, is a matter of content and of content alone. 

The Hypothetical Necessary or Relative aspect of judg- 
ment is a consequence of the designation of the subject by 
any determinate ideal content. It is the universal con- 
nection of attributes within systems, as opposed to the 
morphological unity of individual systems upon which 
that connection rests. This aspect is undoubtedly per- 
ceptible from the moment that the immediate subject is 
made explicit by help of ideas, but as long as there is a 
gulf between the ideal content and the latent reality which 
it designates the 'this' the necessary aspect of the 
judgment is absolutely dissociated from its categorical 
aspect, and the divergence almost amounts to a duality of 
the judgment. In some cases indeed the contents employed 
to designate the subject will have only a partial connection 
with the predicate, as in ' This flower is a rose V Such a 
judgment has been called a double appellative judgment. 
But I incline to think that affirmation of this type is always 
on the road to necessity ; ' flower ' does not indeed tie down 
the predicate to ' rose,' but the thread of botanical classifi- 
cation runs through both. If it were not a flower it could 
not be a rose. So the two designations are undoubtedly 
chosen with reference to one another, and the true duality 
of the judgment is not in christening the rose twice over as 
rose and as flower, but in the ambiguity between ' This is a 
rose ' and ' This, if (or ' in as far as ') it is a flower at all, is 
a rose,' which might well be said of the Tudor rose as it 
appears in some decorative designs. 

The judgment whose subject is designated by a proper 
name is at first sight devoid of necessity. For in it deter- 
minateness of content is sacrificed to the indication of actual 
continued individuality, and therefore the relation of neces- 
sity or hypothesis, which depends on determinateness of 
content, is not easily traceable. Yet a name is always 

1 Cp. Sigwart, vol. i. p. 62. 

150 Quantity and Proportion. [booki. 

eapable of acquiring a definite content, which at once 
brings such a relation into prominence. The indignant 
denial, ' Gladstone never said that,' ' Socrates never gave 
immoral advice,' is obviously hovering between the sense 
of 'A. B. did not go to town to-day' and that of 'An 
honest man cannot say what is certain to mislead,' that is 
to say between the assertion of fact and that of necessity. 
And again, if, as explained in the last paragraph, the 
content which designates the subject has not the nature of 
a complete or individual whole, then its reality must be 
taken as that of which alone it is capable, viz. indefinite 
presentation in the series of space and time ; and this 
amounts to so little (for the presentation may be as rare as is 
consistent with occurring at all) that the element of necessity 
or relativity dominates the element of unity or actuality, 
and the judgment appears to have as its essential content 
a necessary sequence or connection about the presence of 
which in reality little or nothing is affirmed. Such a judg- 
ment, and every judgment in as far as it can be thus regarded, 
is hypothetical, that is to say it runs wholly or partly along 
a line which may be formulated as ' If a is (or in as far as a 
is), then b is (or so far b is)/ 

On the other hand, even those perceptive or historical judg- 
ments, including ordinary assertions about people or places 
called by proper names, which betray in their content no 
tendency to enter a groove, i. e. to exhibit a universal con- 
nection of attributes, nevertheless must be held as bound by 
this ideal, which is involved in the employment of contents 
which have a meaning, and therefore can acquire a de- 
terminate meaning. If then, as in such instances we may 
assume to be the rule, the contents actually employed in 
judging embody no principle, but merely exhibit irrelevant 
differences as coexistent in a concrete subject, such judg- 
ments, even when true in their first meaning as mere 
statements of fact, are yet fundamentally false. That is to 
say, they are true in their categorical aspect but false in 
their hypothetical or relative aspect, from which, being 

chap, in .] Universal = Hypothetical ? 151 

definite judgments, they cannot escape. They do not 

express an a, upon which, within some real system, the 

content of predication follows as b. But it is important to 

remember that we are dealing from beginning to end with 

aspects and not with total differences. I believe that 

a misapprehension on this head has of late years given rise 

to an erroneous conception regarding the tendency and goal 

of knowledge. 

vii. It is a great thing to have raised the notions of Logic Knowledge 

to a level with the ideas of exact science. This has been absolute 

done by Mill and subsequent writers \ and the work had and rela- 

become necessary, though the views to which it led were 

not in principle new. The essence of judgment was by 
them declared to lie in the coexistence and rational con- 
nection of attributes, and the ideal of science to consist in 
the knowledge of the fewest assumptions, from which, if 
given, the whole course of the world might be deductively 
derived. As a consequence of these ideas, the universal 
judgment was, in part by Mill himself and more distinctly 
by later writers, identified with the hypothetical or abstract 
affirmation of necessary connections ; and, further, by iden- 
tifying this type of judgment with the extreme case of 
supposition for the sake of argument, the universal judgment 
as such was denuded of all affirmation having real content. 
It was still treated as affirmed of Reality, but was held to 
be related thereto as a known consequent to an unknown 
antecedent. It was pointed out that in supposal for the 
sake of argument no element of the content supposed or of 
its consequence is affirmed either to be actual or even to 
be possible, and that nothing more is alleged as fact, in 
judgment based on supposition, than that Reality, which 
itself does not appear within the judgment, is such as under 
the supposed conditions to exhibit the inferred consequent. 

1 Mill's Logic and Lotze's earlier Logik seem to have appeared in the same 
year (1843). Lotze, I presume, was largely influenced by Herbart on the point 
in question. I have in my mind also Sigwart, Wundt (whose doctrine of ' Gegen- 
standsbegriff ' does not however seem to me perfectly clear), and Bradley. 

152 Quantity and Proportion. [booki. 

Truth, it might therefore be concluded, may be taken to 
illustrate, but it cannot be taken to define, reality. The 
strong implication of actuality which attaches to the content 
of many ordinary universal judgments was dismissed as 
explicable on grounds of habit and confusion. Thus the 
categorical judgment, in the sense of a judgment which 
asserts any specific content to be actual, was primarily con- 
fined within the limits of affirmation about individuals in 
space and time, although in disjunctive judgment, and in 
judgments, if any, dealing with existences beyond time 
and space, a categorical character was admitted to reassert 

In contrast with the conception of logical progress and 
with the ideal of knowledge which I have just described, it 
appears to me that a somewhat modified form of the 
views in question might yield less one-sided conclusions. 
I should prefer to regard the normal and central evolution 
of judgment as categorical from beginning to end, and as 
gaining, not losing, in this characteristic as it passes from 
perception and history to the more complete forms of 
science. The implication of real existence which attaches 
to the content of ordinary generic and universal judgments 
seems to me to be of the same kind as the implication of 
existence for it is no more which accompanies the 
demonstrative ' this,' ' here,' or ' now,' or its expansion 
by a significant idea, or a proper name, or the significant 
name of any actual, even if not in the full sense individual, 
totality, such as the English nation, or the Natural Order 

The main function of judgment would then be identified 
with the exhibition of individual totalities at once in their 
absoluteness and in their relativity. We should thus not 
wholly subordinate classification, type, and individuality 
to the claims of explanatory theory, but endeavour to 
represent the two as complementary and indispensable 
aspects of knowledge. Abstract- and ideal judgments 
like those which embody the necessary connections of 

chap. in.] Transition to Abstract Quantity, 153 

geometry we should rank as an indispensable divergence, 
but still as a divergence, from the natural track and 
tendency of reason, and as attaining their truth most fully 
when, returning towards that track, they are taken up into 
the precise determination of typical structure in space, or 
even of individual realities. We should refuse, in spite of 
identity in linguistic expression, to take supposition for the 
sake of argument as the type of universal judgment, and 
should point out that as supposition passes from selection 
within reality into free imagination it becomes detached 
from the real ground of all relations, and ceases even to 
exhibit a necessary relativity. 

It is in accordance with these views that I have treated 
measurement as involving both the revelation of Individuality 
(morphological unity) through characteristic ratio, which is 
the same thing as proportion, and the exhibition of relativity 
by the reference of the unit to something outside the indi- 
vidual. I now proceed to speak of kindred judgments, which 
present the essential aspects of measurement in one-sided 


Measurement {continued) Abstract Quantity. 

One-sided 2. Individuality as revealed in measurement may be 
Measure- simple or complex, and, if complex, it must involve a variety 
ment. Q f simple factors. In a simple individuality, or the simple 

factor of a complex individuality, the qualitative distinct- 
ness of the parts is at a minimum ; for any exceptional 
qualitative difference in any part would challenge measure- 
ment and constitute a complication within the unity. When 
an individual is thus taken in its simplicity, in a single aspect, 
and' yet considered as being a whole complete in itself, it is 
treated as a whole of quantity ; that is to say, such a content 
as is exhibited in the predication of the comparative judg- 
ment, but taken as standing in the place of the individual 
Subject, now that the conception of individuality is attained. 
Enumera- i. In such instances we find the simple quantitative whole 
which is thought of as constituted by absolutely homo- 
geneous parts an idea which we have seen to be never 
strictly true, for without some distinctness of quality the 
parts would cease to be. Such a whole differs from the 
normal individual by the lack of anything that can be 
called dominant, essential, or characteristic within the con- 
tent itself. There is, for instance, no need to consider its 
unity in the light of a secondary or aesthetic quality. 
The unity is already that of a continuous quality, and in 
the attempt to define it, it lapses almost wholly into relati- 
vity, for the determination of the whole depends on the 
equation of the parts, in an unending series, with other and 
independent standards. Thus the purely quantitative 
whole is characterised by being capable of construction 
by ideal repetition of a unit or fixed part ; and such ideal 
repetition is enumeration. Enumeration may seem prior 


Enumeration and Measurement. 155 

to measurement or identical with it ; in measuring we 
enumerate units, and whenever we enumerate units we 
measure some totality. When we count the carriages in 
a railway train we are measuring the train, when we count 
the sheep in a flock we are measuring the flock, just as 
when we count the feet and inches in the length of a room 
we are measuring the room. But usage, as we feel at once, 
does not bear us out in speaking of the two former in- 
stances as measurements, and the reason is plain. In 
measurement we start from a whole which we characterise 
by its differences ; in enumeration we start from a distinct 
unit, out of which we desire to construct a collective or 
aggregate whole a sum total. The whole in enumeration, 
which is a predicate, is a weakened form of the individual 
whole in measurement, which is a subject ; and the unit in 
enumeration, which is a subject (generally distinguished by 
a natural individuality), is a strengthened form of the dis- 
tinct unit, ideal part, or constant difference, which forms 
the predicate in measurement. 

Enumeration is therefore in one sense posterior to 
measurement, because it presupposes, as a naturally 
distinct unit, the 'thing,' the idea of which can only be 
furnished by a sense of proportion or perception of 
limit ; but, on the other hand, enumeration is an instru- 
ment of precise measurement, which involves the notion 
of a scale of degrees or aggregate of homogeneous parts. 
The two processes are constantly concurrent, and only 
differ in the respective values of the parts and wholes 
with which they deal. It would be futile to distinguish 
them from one another, but for the consequences which 
result from the possibility, first exemplified in abstract 
enumeration, of systematising the synthesis of parts without 
relation to a whole. The whole of enumeration is depressed 
into a mere aggregate, or not even a definite aggregate, and 
therefore the part into a mere unit, or even into the mere 
place in which a unit might be. The process with all its 
corollaries, including the three unreal infinities of Number, 


156 Abstract Quantity. [booki. 

Time, and Space, must be regarded as belonging to a form 
of the judgment-function in which the relation of whole 
and part is denuded of all structural variety, and therefore 
the aggregate or sum which is the outcome of that relation 
lacks predominant unity. This principle is expressed in 
the saying that in a numerical system the sum of units is 
the same whatever may be the order in which they are 
counted, i. e. any part {qua part of a total formed by 
enumeration) can be interchanged with any other part 
without modifying the whole in which they are parts. 

Corollaries. I proceed to state and illustrate some corollaries which 
follow from the above idea of enumeration. 

Simple a. Simple counting always consists of a series of singular 

ng. judgments % and is in this respect on a level with simple 

However abbreviated or abstract each step in counting 
may be, it can always be expanded into a singular judg- 
ment which records its own position in a coherent series. 
In counting the birds in a covey, or the stitches in a bit of 
needle-work, we often merely repeat aloud the words ' one,' 
1 two,' 'three,' and the real nature of the judgment which 
accompanies them is open to question. In fact, each of 
these numerals in such a case implies a separate singular 
judgment, though extreme abbreviation tends to conceal its 
structure. The essence of counting is in just such a pro- 
gressive distinction as is conveyed by 'this/ 'that,' and 
' the other ' ; ' alter ' and erepos have almost the value of 
numerals. The exclamation ' One ! ' when we are begin- 
ning to count any set of objects means ' This unit is a part 
in the whole which interests me,' e. g. ' One two three 
eight birds in that covey.' The bird is the naturally distinct 
unit by which in so simple a case we proceed as a matter of 
course, and the covey is the total up to which we wish to 
count. If birds get up belonging to another lot, we shall 
probably desire to keep them distinct, and so count them 
separately, beginning 'One,' 'two,' etc. over again. It 
is plain in this or any similar instance that we do not 

chap. iv.] What do we count? 157 

count right on as long as units can be found, but that every 
step of the enumeration is made with reference to a limit as 
well as to a unit. This limit, however disguised by our 
caprices and interests, is simply the common or continuous 
nature of the unit in so far as it interests us, and in every 
enumerative judgment without exception the elements of 
separate unit and common nature may be traced. The 
unit need not be externally distinct or physically separable ; 
and the common nature, instead of being hard to trace, 
may all but obliterate the differences that exist within it. 
But it is the nature of the unit that furnishes both rule and 
limit of enumeration, which is a process unmeaning without 
a limit and impossible without a rule. If we are told to 
count even all the ' things ' in a room, we shall find ourselves 
obliged to ask what is to be reckoned as a ' thing.' Is a book- 
case with 500 volumes in it one thing or 500, or 501 ? 'In 
a room,' however, is a kind of limit, and assigns a totality 
to be constructed by synthesis ; but if we are asked simply 
to count, we should reject the request as pure nonsense, 
because it assigns no totality to be constructed by counting. 
What, then, is the meaning of counting ' One ! ' ' Two ! ' 
1 Three I ' in starting a race, or of 

'And still stood all who saw them fall 
While men might count a score ' ? 

In the latter case, the idea is that of counting the names of 
the numbers up to a fixed limit at a rate determined by 
habit or by the time which is required to pronounce the 
words distinctly. In the former case the object is perhaps 
not merely to let time elapse, but to set attention in a 
certain rhythm, so that the tendency of rhythmical antici- 
pation may assist in seeing or hearing the starting signal 
at the moment it is given. For this purpose the periods 
should be exactly equal, and in fact at the Oxford boat- 
races every boat has some one beside it who counts aloud 
the last few seconds before the gun fires. Of course, finally, 
the names of numerals may be repeated, as any words 
may, without a meaning. But to do this is not to count. 

158 Abstract Quantity. [bookt. 

Thus even simple counting always involves the elements 
of the judgment of an identity exhibited in differences 
and affirmed of reality; which elements present themselves 
in the shape of a distinct unit within a continuous nature, 
its relation to which nature is indicated by number. And 
that the simple enumerative judgment is always singular 
follows from the nature of the unit, which is theoretically 
nothing more than the content to which we ascribe dis- 
tinctness pro hac vice-, in other words, the unit is the 
difference or part that is taken as distinct by one act of 
judgment, and it may be said that what we count in 
enumeration are primarily the acts of judgment, as acts of 
distinction and relation within a certain continuous quality. 

Does it follow from this view that Number arises 
essentially out of the sense of time or succession ? I answer, 
Not .' essentially.' The connection between number and 
succession is a psychological and not a logical question. 
If it is impossible for two related acts of judgment to be 
simultaneous, as we are naturally inclined to suppose that it 
is, then two enumerative judgments must always be suc- 
cessive, and in this sense enumeration may depend upon 
succession. Nor do I think that this connection is necessa- 
rily disproved by such observations as that perception can 
take note of six balls at once being dropped into a box. 
Such a perceptive judgment, in my opinion, is probably 
one, and applies the result of previous counting, as an attri- 
bute resting on experience, to the perceived content, just as 
we can judge the number of pips on a card from the mere 
form of the pattern which they make. So if we count by 
twos, fours, or more, I think that this is complex counting, 
the unit being the mass of two or four, known to be such 
by previous experience 1 . A logical order among the units, 
i. e. an order in which the apprehension of each unit has a 
place in the series conditioned by the separate apprehension 
of other units, is of the essence of enumeration, although a 
material order among them, i. e. such an order that a unit 

1 Vid. the Author's Knowledge and Reality, p. 92. 

chap. iv.] Number and Magnitude. 159 

changes its value by changing its place in the series, is in 
contradiction with the essence of enumeration. Unless 
there is what I have called a logical order, we have no 
security that the unit as such is apprehended at all, and 
what we take for enumeration may really be an inference 
like that which detects from the pitch of a note the number 
of vibrations per second which generate it. But whether a 
logical order of succession can only be realised in tempo- 
rally successive acts of apprehension, is a purely psycho- 
logical question ; the more so, that, as we have seen, 
succession and time do not exclude unity of judgment, and 
the acts of judgment which constitute an enumeration 
might even, like an inference, be brought under the head 
of a single continued state of consciousness. In any case, 
succession in time would be a mere psychical condition of 
number, following from the unity of the intelligence as 
forbidding (if it does forbid) two judgments to be made 
at once. There is no sort of ground for connecting enume- 
ration with the apprehension of equal parts in time, unless 
the equality of such parts be the material purpose of the 
apprehension in hand. 

/3. It follows from the nature of enumeration that the Discrete 
distinction between discrete and continuous magnitude # ^ tlnuous." 
the opposition of number as discrete to space, time, and other 
kinds of quantity as continuous, rests on a confusion. 
Number as mere names or mere sounds may be discrete, 
i. e. disconnected, but then it has nothing to do with magni- 
tude, but is a set of mere words destitute of meaning. On 
the other hand, number considered as the vehicle of magni- 
tude or quantity is both discrete and continuous ; and the 
same is true of all quantity, as we saw in examining the 
comparative judgment, and it is the essence of quantity 
to be so. The distinctness of natural units such as recipro- 
cally exclusive material things does not make any difference 
of principle. They, like all units, are numbered in virtue of 
a continuous quality or identity which pervades them, and 
every unit, though it may only be suggested by a mo- 

160 Abstract Quantity, [booki. 

mentary purpose, is, like them, a distinguishable part, 
within a whole or aggregate consisting of such parts. The 
books on a shelf are not merely discrete, and the inches in 
a yard or the units of weight in a gravitating body are not 
merely continuous ; in every case the unit is a distinct or 
discrete part, and the sum is a self-identical or continuous 
whole. It is nonsense to speak of counting without saying 
what is to be counted ; and in specifying what is to be 
counted we specify at once the nature of the continuity and 
the rule of the discretion, 
judgments ii. Judgments affiliated to the Enumerative Judgment, 
Enumera- The Enumerative Judgment is the root of all quanti- 
se Judg- tative determination ; and, as we have seen, all the matter 
of knowledge above the stage of pure quality is either in 
itself or in its conditions accessible to quantitative deter- 
mination. But the judgment in question also contains, that 
is to say, &, though in a depressed form, the universal 
essence of judgment in the principle of identity and differ- 
ence ; and it is possible for this to be revived by one kind 
of abstraction into a different relation from that of unit and 
sum, as it is for it to be further specialised, by an opposite 
abstraction, into an idealised form of the latter relation. 
But before indicating the genesis of other types of judg- 
ment out of enumeration, we must glance at those which 
it necessarily generates, and which must be regarded as 
species of itself. These are, a. the Plural or Particular, and 
/3. the Collective judgment. 
The Plural a. The Plural Judgment, or the Particular of traditional 
lar JuS? Lg* c > differs in no essential respect from the singular. It 
ment. is not however accurately described as a mere aggregate 
of singular judgments, and indeed this description does not 
explain itself, for is such an aggregate several judgments or 
only one ? I cannot doubt that the plural judgment is a single 
act of thought, which determines a certain whole or aggre- 
gate, given at the moment, though, it may be, in process of 
modification, by an attribute or condition such as two, three, 
or some other numberwhich expresses the reciprocal relations 

chap, iv.] Plural implies Ratio. 1 6 1 

of its homogeneous parts. Thus the plural judgment is not 
an aggregate of judgments, but a judgment about an aggre- 
gate. Therefore the number is to be regarded as a predi- 
cated content or determining condition, attributed to a whole 
consisting of the units which have been counted up to the 
point at which the plural judgment is taken. That the 
element of continuity, or designation of the whole whose 
parts are to be counted, must quarrel with a determination 
by any number short of this whole \ and demand a con- 
tinuance of the enumerative process, is only a case of 
what happens in every judgment of perception. Such 
judgments, as we have seen, never embody 'pure cases,' 
i.e. they never fit precisely into a groove of necessity, 
that is, a sequence of reason and consequent. There is 
always something relevant omitted, or something irrelevant 

Thus the particular judgment from the very first implies 
a ratio ; and the implication may be so strong as to take the 
judgment out of the category of particular judgments and 
place it in that of collective judgments, e. g. ' 335 members 
of the House of Commons are Liberals.' As every one 
knows that the House of Commons contains altogether 
670 members, this is just the same as to say 'half of the 
House of Commons are Liberals.' It depends for its 
meaning on a completed enumeration, and therefore is 
essentially a collective judgment. It may even be re- 
garded as an instance of simple measurement, i. e. of ratio 
treated as pure historical fact, in as far as its purpose is to 
measure the voting power of the Liberals against that of 
other sections of the House. The Liberals and the whole 
House are equated in respect of numerical strength ; the 
whole House minus half of the whole House = the Liberals. 
In short, as we have seen, the completed judgment of 
Enumeration passes into Measurement, though the idea of 
Measurement is prior to the act of Enumeration. If on the 
contrary we say that 'Two Cambridge men are coming 

1 See Knowledge and Reality, p. 65, and above, Introduction, pp. 54 ff. 
VOL. I. M 

1 62 Abstract Quantity, [booki. 

down to lecture,' the number two is prima facie non-signifi- 
cant ; the judgment tells us nothing of the ratio borne by two 
to the whole number of Cambridge men, nor even to the 
whole number of local lecturers. Nevertheless if we think 
of it, we shall see that either it was wholly superfluous to 
mention the number, or else some context or latent allusion 
must imply a ratio. Number has significance only by 
comparison with number. 

The Plural Judgment is equivalent to the Particular of 
traditional logic in the form ' Some men are mortal.' There 
is no essential difference between ' some men are mortal ' 
and ' four men are mortal ' ; the two assertions, if interpreted 
literally, belong to the same logical class. It will appear 
however below that this literal interpretation does not 
render the true meaning of the old ' Particular Judgment 1 .' 
But we must distinguish from the above a form which 
has been employed in quasi-numerical arguments, viz. the 
form ' Most men are mortal,' or ' The majority of the House 
of Commons that has just been elected is Conservative.' 
These judgments are not merely particular even in immediate 
appearance. They present on their very surface the relation 
to a collective judgment which we saw to be at least latent 
in every particular affirmation. 'Most' or 'The majority' 
means more than half; and when we speak of half or a 
quarter or any ratio we assume a completed enumeration 
of the whole. We must therefore now pass to the Collective 
Judgment or Judgment of completed Enumeration. 
The Col- P m The Collective Judgment has of late been rightly dis- 
kette tinguished from the Generic and from the Hypothetical 
Judgments, which correspond to the real meaning of the 
Universal Judgment known to traditional logic. It has 
been justly pointed out that the 'All ' of mere extension or 
numerical totality does not really express what is intended 
by such an allegation as 'All men are mortal,' or 'All triangles 
have their three angles equal to two right angles.' In such 
cases complete Enumeration is inconceivable, and something 

1 See on ' Modal Conversion,' chap. 7, below. 


chap, iv.] Meaning of "All" 16 

quite different, viz. the universal connection of attributes 
which are not results of enumeration (for number is also an 
attribute) is really the matter affirmed. So far all is clear, 
and Logic has greatly gained by the distinction. 

But when we come to erect a difference of kind, and to 
treat the collective judgment as purely on a level with the 
singular or particular judgment, and as in fact a mere 
aggregate of singular judgments, and as thus separated by 
an impassable gulf from the universal judgment ; and when 
we further maintain that enumeration cannot warrant its 
own completeness, then we fall into difficulty and confusion. 
Even the Plural Judgment, as we saw, is not a mere aggre- 
gate of singulars. 

The Collective Judgment I understand to be a judgment 
made about a definite group or limited class of individuals, 
which individuals are taken to have been exhaustively 
enumerated, or to be capable of exhaustive enumeration. 
It is not necessary that the individuals should all be 
together in space or time ; it is not necessary that they 
should all exist or have existed with any specific degree of 
reality ; but it is necessary that every one of them should be 
brought before the mind, or should be capable of being 
brought before the mind, in a distinct and separate enumer- 
ative judgment. Such judgments are 'All the books on 
that shelf are German,' Every horse that I have bought 
in the last three years has gone lame,' 'All the kings of 
England since the Conquest but three have died natural 

When it is said that such judgments as these are on a 
level with the singular or the particular judgment, I take 
it that we must exclude from the meaning of singular or 
particular judgment all dependence, whether latent or 
explicit, on completed enumeration ; otherwise our account 
of the collective judgment becomes circular. But if so, 
then we have the ' allness ' of the collective judgment staring 
us in the face as a distinction between it and the particular. 
And this distinction becomes an absolute severance if we 

M 1 

164 Abstract Quantity. [booki. 

are to insist that the process of enumeration, a process which 
consists in singular and particular judgments, cannot furnish 
the warrant of its own completeness. 

I have maintained elsewhere 1 , and it follows from my 
whole conception of the judgment, that enumeration cannot 
be made intelligible on such a view. It is impossible for 
enumeration to go on apart from the discriminative control 
exercised by the pervading nature of the totality under 
construction upon the successive apprehension of the units. 
It is this control which takes the form of an inchoate per- 
ception of ratio as the counting advances, and of the warrant 
of exhaustiveness when it is completed. Apart from such 
an influence of the whole there can be no purpose in 
enumeration. No doubt therefore complete enumeration is 
in one sense on a level with the singular and particular 
judgments, because they present though in an imperfect 
form (as we have excluded the case of definite ratios such 
as ' Half A are B') the same relation to totality which the 
collective judgment completes. 

But for the same reason it is impossible to justify an 
absolute separation between the collective and the generic 
or universal judgment. The collective judgment, we may 
say, must emanate from an enumeration of actual indi- 
viduals, or at least of individuals actually brought before 
the mind, one by one. But how can we carry a genetic 
distinction like this into the interpretation of judgments 
whose actual content is precisely the same? It is the 
commonest thing in the world for a judgment to be taken 
as exhausting a group or set of distinct individuals, without 
resting in any way upon direct enumeration ; in other 
words, a judgment that might be obtained by enumeration 
constantly is obtained in some other way. The fact is, 
that when we have gone beyond sets of individuals present 
to perception or within the power of the mind to represent 
at once as distinct individuals (and no one could possibly 
propose to limit the collective judgment to such sets of 

1 Knowledge and Reality, p. 77. 

Chap, iv.] Unity of an Aggregate. 165 

individuals), we have entered on a process which is plainly 
and obviously mediate and hypothetical, and the fact that 
many judgments thus mediated are taken to refer to a finite 
group of individuals is a mere instance of our general rule 
that every content in judgment is taken to have the reality 
of which it is capable. 

Is there then no difference between a collective judgment >/ 
and a true universal ? Certainly there is a difference, and 
it is illustrated though not constituted by the connection 
of the former with complete enumeration. It is simply this, 
that a collective judgment deals with a content which can be 
presented to thought as possessing the character of an aggre- 
gate of exclusive units, or finite whole of enumeration. This 
point of view would involve identification of the collective 
judgment with the aggregate of singulars only if all enu- 
meration were simple enumeration. But a numerical whole 
may be obtained by mediate enumeration, and it is to 
a whole so obtained that the content of many collec- 
tive judgments is equivalent. It is true that a collective 
judgment is not a genuine universal, but it is not true that 
such a judgment must be equivalent to a mere aggregate 
of singulars. This conception is, in the first place, irrecon- 
cilable with the unity of the judgment 1 ; and, in the 
second place, is not warranted by the plain meaning of the 
propositions in question. It is impossible to designate a 
number of individuals by a common name as the subject of 
a judgment without implying a significance in the designa- 
tion. Even if the predication is true of the different indi- 
viduals for different reasons, the common interest of the 
judgment must give it unity of purport. An arbitrary 
limitation either of number or of time tends, no doubt, to 
interfere with this significance, and to force an extensional 

1 No doubt there is a difficulty here. ' George and John have gone to school,' 
1 The two boys have gone to school.' Does the former sentence convey two 
judgments and the latter only one ? The latter only one, certainly ; the former 
conveys two at first sight ; but if we bear in mind our account of the Judgment 
as an act in time, we shall see that these two may readily pass into one. See 
p. 85, supra. 

1 66 Abstract Quantity. [book i. 

meaning upon the judgment ; but, as we know, the purest 
extensional meaning is only a minimum of intensional 
meaning. And there are collective judgments which could 
not possibly be taken as mere aggregates of singulars. 
Such are reflective historical judgments. 'All States of the 
North American Union are prohibited from interfering 
with the tenure of property.' I need not know this by 
simple enumeration ; I may know it mediately, as a pro- 
vision of the Constitution of the United States. I need not 
even be actually able to enumerate the States which are 
included in the Union. But I know that they are numer- 
able, because I know that they are an actual limited 
group, and so I judge it as a historical fact, though I may 
know it also as rooted in the nature and tendencies of the 

The fact is, that superficial as is the view which makes 
' allness ' the adequate expression of logical necessity, it is 
if possible, more superficial to deny their connection. From 
the first use of the designative idea, necessity makes itself 
felt ; and ' allness/ or the aspect of a finite totality as an 
aggregate of exclusive units, is never without a warrant and 
significance however arbitrarily the totality may be taken. 
It is by the certainty of complete enumeration that count- 
ing becomes, as was said above, the organon of precise 
measurement. For instance, the series of enumerative 
judgments, ' One, two, three, four, five, six ounces are in 
the scale balancing this packet,' is convertible, in virtue of 
their exhaustiveness, into the judgment of measurement, 
' This packet weighs 6 oz.' 

We saw that the act of counting tends to assume inde- 
pendence, as if it could have a meaning apart from any 
continuous nature in the units, i. e. in short, apart from an 
identity presented as a totality. This is not merely owing 
to the customary abbreviation of the enumerative judgment, 
as when we seem to count by saying ' One, two, three,' etc. ; 
rather such an abbreviation is made possible by the appa- 
rently independent reality of number. This appearance of 

chap. iv.] Abstract Number. 167 

reality depends on the fact that the numerical series does 
furnish a generalised scheme of the relation of whole 
and part when envisaged in the form of total and units. 
Such a generalised scheme, though meaningless except as 
applied to a positive content of thought, contains neverthe- 
less definite and necessary relations which are imposed by 
it on any content to which it is applied ; and the pre- 
supposition that it is taken as applied to an adequate 
content fades into forgetfulness that it need be applied to 
a content at all. But need it? We may surely investigate 
the numerical series for its own sake. When we say that 
twice 50 is 100, need we mean that twice 50 of some parti- 
cular kind of thing are 100 of it? We may surely mean 
that in the numerical series 100 is separated from 50 by the 
same number of places as 50 from o, which relation involves 
a variety of consequences, all true of the numerical series 
as such. No doubt this is so, but it will be observed that v 
we have to appeal to the idea of places in the series, and 
these places are the abstractions of enumerative judgments 
and imply relation to a content. Such places contain in 
themselves no reason for stopping at any point of enume- 
ration, are applicable hypothetically to every content, 
but can yield, in their abstraction, no conclusion about any. 
It is a well-known fallacy to obtain a concrete estimate by 
multiplying an amount by the number of times its cause as 
given has to be repeated. Hardly any concrete quantity is 
unaffected in the ratio of its increase by a great addition to 
its absolute magnitude. To say that the stock or trading 
capital of England is worth so many hundred millions 
sterling is a graphic expression for the fact that its amount 
is a million times as great as an amount worth so many 
hundred pounds. But in the economical sense of ' worth ' 
the conclusion is nonsense. A thing is only worth what 
it will fetch, and who is going to buy the whole stock of 
England if thrown on the market at once, at the rate which 
is commanded by the amounts of stock which change hands 
in the common way of trade ? 


Abstract Quantity. 

[Book I. 

tion be- 

The numerical series is an ideal scheme of the relations 
of units within totals, but is itself unreal apart from its 
applications, not because it is ideal, but because it has in 
itself no element of limit or totality ; i. e. its units make no 
choice between belonging to one total and another, and so 
naturally belong to an infinite series. 

This aspect of the enumerative judgment the system of 
number leads to the consideration of complex counting 
and of numerical infinity. But before pursuing the enquiry 
in this direction I pause to indicate a reversion or conver- 
gence to which the simple enumerative judgment tends in its 
other aspect. 

y. Every concrete enumerative or collective judgment 
bears reference to an identity which controls its selection of 
units and fixes the limit of its enumeration. This identity 
The i s the pervading nature of the units. Now if this nature 

I xll 8, XX S 1 1 V C 

Judgment, consists in the characteristic quality of an individual thing, 
then it is possible that on the one hand it suggests no con- 
ceivable limit of enumeration, while on the other hand the 
characteristic individuality claims completion in respect of 
its positive connections of content. In such a case there is 
no true whole of repetition concerned ; no whole, that is to 
say, which in its nature draws nearer completion by every 
repetition of an individual. The books in this room are 
a true whole of repetition ; the human race, to our present 
knowledge, is not. Thus a problem which is first attacked 
by enumeration may transform itself unawares. Meeting 
with a series of individuals in which we perceive some 
important attribute, we enumerate them as cases of it. But 
soon their characteristic nature reacts on the function of 
thought, and we find our successive judgments attempting 
to grasp a connection of content and not to exhaust a sum 
total of cases. Now as enumeration is on one side selective 
analysis, we continue to give our judgments enumerative 
form, and even couch them by anticipation in the shape of 
exhaustive totality. Then we have what has been called 
Induction by simple enumeration, with its results embodied 

chap. iv.] A further meaning of "All" 169 

in the Judgment of Allness, which to avoid an un-English 
expression I shall venture to speak of as the Exhaustive 

The most varied opinions have prevailed as to the nature 
and value of this process, obviously because it forms a tran- 
sition between two distinct lines of thought, marking the 
revival within mere enumeration of the sense of characteristic 
individuality which belongs to the judgment of proportional 
quality and the kindred judgments of individualising thought. 
We meet, for instance, with the question whether the judg- 
ment i All men are mortal ' claims to represent completed 
enumeration or not.' The answer is that its form and its 
meaning are at variance ; in form it does make this claim 
and in meaning it does not. Such a judgment indicates 
that the spirit of analogy and of characteristic quality has 
reawakened within the form of mere enumeration, and is 
sweeping the line of evolution back towards judgments 
which predicate individual and generic character. When 
we come to speak of Induction as a phase of Inference we 
shall see that there are good reasons for such an awakening. 
At present we have only to note that the exhaustive judg- 
ment ' All men are mortal ' is a transitional form between 
a collective judgment on the one hand, and the generic 
judgment ' Man as such is mortal,' also couched in the form 
' All men are mortal,' on the other hand ; and arises from an 
incipient reaction of positive content upon ideal schematic 
form in the process of making number, before an external 
separation has been effected between the two elements. It 
is idle to demand the perfection of complete enumeration 
from the exhaustive judgment ; for this latter is a popular 
and unstable form of thought, and must simply be recog- 
nised as such. It is better to treat the collective judgment 
as inevitably leading up to a connection of attributes and 
as therefore having its ideal in the spirit of the exhaustive 
judgment, than to interpret the exhaustive judgment 
according to the letter, as having its ideal in the collective 
judgment. We shall have to recur to this subject when 


170 Abstract Quantity. [Booki. 

we return to the central development of the judging 

We have now to trace the further abstractions which have 
their root in enumeration. 
Judgment 6. On the side of the relations between units and total as 
Counting sucn > abstraction being made from the positive nature of the 
contents submitted to enumeration, the- judgment of com- 
pleted enumeration is an ideal or generalised scheme of all 
possible constructions of such purely numerical totalities. 
It starts from a measurement or collective judgment of the 
type ' All the books in this room amount together to a 
thousand.' The further abstract development of such a 
predication may be brought about by the most various 
occasions, but it essentially consists in this, that the positive 
concrete units of enumeration which stand as subject in a 
J judgment like the above- are replaced by generalised rela- 
tions of ideal units equated to a total which also becomes 
ideal and generalised. This substitution reveals the fact 
which alone makes it possible, viz. that in the numerical 
scheme all units, being abstract, retain the same value in 
every part of the series ; e. g. the units between 50 and 60 
count for as many as and no more than those between 30 
and 40 or between o and 10. Thus a series of units may 
safely be named by the number of places which it occupies 
counting from the zero of the whole numerical series, but it 
is the same wherever and however often it recurs. It is on 
this characteristic of number that the possibility of mediate 
or complex counting and of equation, which is implied in 
these processes, depends. If, for instance, we desire to re- 
compose the sum of books in the room by equating it to 
component sums or to factors, we do so by conducting a 
number of enumerations separately from the beginning of 
the numerical series, and then combining their totals 
according to the rules of that series, which are known to us 
simply by experience. Thus, if we count 700 English 
books, 200 German, and ico Italian, we find that these 
sums, considered merely as numbers, are equal to the total 

chap, iv.] "Mediate" and "Abstract!' 171 

1000 obtained by direct enumeration. * Considered merely 
as numbers,' because the rules of the numerical series cannot 
warrant us against any material influence of the actual 
individual things upon each other. Some of them may 
cancel each other, or may produce more by combination ; 
but this has nothing to do with the properties of number, 
except for the fact that, when known, it is capable of 
numerical expression. The component numbers in the 
subject of a judgment like the above (These 700 English 
volumes with these 200 German and those 100 Italian make 
up 1000 volumes) correspond to the designative ideas in an 
affirmation like ' This execrable ruffian should be hung.' It 
is hard to say if they are general conditions, or if they are 
specifications of fact taken as true merely in the present 
instance. -^" 

But it is clear that in such enumerations we are on the 
brink of mediate counting, that is to say of the abstract 
equation 700 + 200+100=1000, just as in the individual 
judgment mentioned above we were on the brink of the 
generalisation ' Every execrable ruffian ought to be hung.' 
' Mediate counting!' it will be said; 'then we are in the 
region of inference, and no longer in that of judgment.' It 
is certain that when we speak of necessary connection 
between attributes, of hypothetical or mediate judgment, 
we are in the region of inference ; but it is not the case that 
we are therefore out of the region of judgment. By 
1 mediate ' in the present connection I only intend to 
designate a judgment which has for explicit subject a 
generalised or abstract attribute, and being free from any 
demonstrative or sign of perception must be taken as 
conditioning its predication by that attribute. Such a 
predication is mediated, i. e. is affirmed of any particular 
individual only through and in virtue of the attribute 
expressed in the subject. Mediate counting forms the 
transition between ratio and proportion just as mediate 
measurement does. Logically speaking every equation 
expresses a ratio, and a ratio becomes a proportion directly 


Abstract Quantity, 

[Book I. 






it is applied directly its unit is taken as variable. Thus 
an algebraical equation, which exists with a view to a variety 
of applications, is ipso facto a proportion. 

Complex counting is a case of mediate counting ; that 
case in which we count by units which are themselves sets 
of numerical places, i. e. by multiplication and division, which 
may for the purpose be taken to include addition and sub- 
traction. The only difference between multiplication and 
division on the one hand and addition or subtraction on the 
other is the equality to each other of the subordinate totals 
in multiplication and division, which enables them to be 
counted as units and their number indicated like any other 
number, by its place in the series counting from o upwards. 
In this sense multiplication is a mere abridgment of addition ; 
it is only a question of form whether we say 2 + 2-1-2 + 2 = 8 
or 2 X4 = 8. This latter equation represents what is essen- 
tial as well in addition and subtraction as in multiplication 
and division, a total analysed into factors and a process. 
Complex counting, as a case of mediate counting, shares its 
abstract, hypothetical, and necessary character. 

e. The processes of mediate counting deal with the con- 
struction and reconstruction of any given numerical total. 
Even the quantitative relation of part and whole in its 
extremest abstraction retains thus much of structural unity, 
that, given a total of units, it can only be dissolved or 
reconstructed according to certain rules of combination or 
analysis. But the quantitative unit per se, or rather the 
one-sided abstraction of the quantitative unit, the mere 
numerical place which no positive identity links with the 
other places of the series, has in it no principle of totality 
or limitation, that is to say no reason for stopping short 
after one set of such places rather than after another. 
Enumeration of units as such may be continued at plea- 
sure, and the process of so continuing it without limit is 
summarised in the conception of numerical infinity. 

We have here tracked to its genesis this paradoxical 
conception, in its right place so powerful for good, and in 

chap, iv.] Progress to Infinity. 173 

its wrong place for evil. It would not, perhaps, be beyond 
the province of logic to comment on its use in its right 
place, that is to say in mathematical science ; nor could a 
more interesting subject readily be found. But lack of 
mathematical knowledge deters me from attempting such 
a comment with any degree of detail ; for a logician is 
aware of the risk incurred by venturing beyond his know- 
ledge, and as he preaches that there is no royal road to 
truth, must keep clear of the delusion that he himself has 
found one. But any one may offer a suggestion, and this 
I propose to do by saying that it seems to me most pro- 
bable that the scientific use of the conception of infinity 
rests in every case on a justifiable neglect justifiable, 
because that which is neglected has a known nature, and 
may be set down as insignificant either altogether or from 
the point of view of a specific purpose. 

If, to take a coarse and non-mathematical instance, we 
set about any task in a way which is demonstrably perverse 
and inadequate, a looker-on is justified in disregarding our 
efforts. He will tell us that we shall not get it done in 
that way if we live to the age of Methuselah. Translated 
into logical phrase, his comment means that our way of 
going to work has not the element of totality; the suc- 
cessive efforts which make up the series of our activity, 
bearing no relation to the nature of the work to be done, do 
not include in themselves successive parts of it, and therefore, 
as regards it, have no tendency to come to an end and will 
(unless we choose to leave off) go on to infinity. We may even 
apply this illustration to a simple mathematical idea, say to 
the case of parallel straight lines. We may consider as the 
task to be accomplished such a change of direction in either 
or both of a pair of parallel straight lines that they should 
cease to be parallel to one another. And we may consider 
as the means adopted to bring about such a change the 
production of the two straight lines in their original direc- 
tion. Then our supposed on-looker would say, ' You might 
go on for ever at that game;' 'You cannot change the 

174 Abstract Quantity, [booki. 

direction of a straight line by producing it in its original 
direction.' Therefore it would be justifiable to neglect the 
production of parallel straight lines to infinity, in other 
words to pronounce that such production cannot alter 
their character as parallel straight lines, i. e. that even if 
produced to infinity (which they can never actually be) 
they do not meet. Probably such a case as this would 
hardly be recognised as an instance of the mathematical 
use of infinity, but in as far as it introduces the conception 
of quantitative infinity as a term in a positive definition it 
would seem to be at least analogous to such a use. 

More subtle and interesting are cases in which the con- 

r^j^^x^ J tinuance of the series makes a difference in the task to be 

performed, but the whole possible difference can be shown 
to fall within certain known limits. These cases, which I 
presume to be of the nature of infinitesimals rather than 
of infinites (both of which must fall under the head of 
'.^t infinite enumeration), may be reduced to the same class as 

*fojf the former if we reflect that in the former also the differ- 

ence fell within known limits, but these were limits of kind, 
whereas we are now speaking of limits of quantity. In 
cases of this second type we know that a series could be 
continued to infinity, and that some difference would 
be made to the problem before us by this being done; 
but, on the other hand, we are aware of a limit within 
which the whole series must fall, and we are therefore able 
to pronounce that the difference which can be made by its 
continuance after a certain point is, at least for our imme- 
diate purpose, a negligible quantity. Such, I take it, must 
be the principle of any process which determines e. g. 
the area of a circle by treating it as between the area 
of a polygon inscribed in the circle and that of a poly- 
gon described about it. So far as I follow the exoteric 
utterances of mathematicians *, the principle of abstraction 
based on a positive knowledge of the capacities of a series 

1 I have in mind more especially Mr. Spottiswoode's Presidential Address to 
the British Association, which unluckily I cannot refer to. 

Chap. iv.] Infinite Number. 175 

must be at the root of the employment of mathematical 

But our immediate business is with infinite number con- 
sidered logically, i.e. with a view to its general place in 
knowledge. And from this point of view we have to notice 

(1) That the idea of infinite number has its genesis in a 
one-sided abstraction, viz. in the notion of counting without 
having anything in particular to count 1 , which corresponds 
to the idea of difference without identity, and of parts 
without a whole. By such an abstraction the enumerative 
judgment is destroyed, the essence of judgment as such 
the exhibition of identity in difference or of the whole in its 
parts being withdrawn from it ; and the names of the 
numbers are turned into a meaningless repetition, the pur- 
pose of enumeration having disappeared. We are no 
longer saying ' One tree, two trees, three trees,' etc., but we 
are merely saying ' One, two, three,' and it is for this reason 
that we need never stop. 

(2) Being one-sided, the idea of infinite number is self- J 
contradictory. The essence of number is to construct a 
finite whole out of homogeneous units. The idea of 
numerical infinity arises from neglecting the continuous 
nature of the unit, and therefore omitting the element 
which alone arrests computation at one number rather 
than at another. Thus an infinite number would be a 
number which is no particular number, for every particular 
number is finite. 

(3) It follows from this that infinite number is unreal. 
This does not mean that there may not actually be more 
units of one kind or another than we can count in the time 
at our disposal or in any finite lapse of time. The state- 
ment deals with the nature of number, not with the extent 
of the sensuous universe. If, to put a common idea coarsely, 
we are asked, ' Supposing that you could travel through 

1 A series which is ex hypothesi infinite comes under the head even if it 
seems to have a positive nature. For its nature ex hypothesi does not deter- 
mine the number of its units. 

176 Abstract Quantity. [booki. 

space for ever, and never come to an end of it, must not 
space contain an infinite number of units? or even if you 
can go on subdividing a given portion of matter for ever, 
must it not contain an infinite number of parts ? ' to such 
questions we could only reply, 'Things or the parts of 
things may quite conceivably transcend our power to count. 
But except in view of a finite goal, number does not help 
us, does not tell us anything, grounds no ratio of parts to 
whole. We should in fact never give up counting any units 
that had interest for us, and should in doing so always be 
at some finite number. But if it could be miraculously 
revealed to us that there was no end, then I think we should 
stop counting, unless the units in question entered into 
subordinate or graduated totals which had an interest 
for us. Thus we go on counting the stars for definite 
reasons. Their relation to us is graduated, and several 
subordinate totals within their number have already been 
completed by enumeration ; e. g. stars of the first eight 
magnitudes have been identified and counted. In counting 
them we have always in view some definable total to be 
constructed or to be corrected. Who counts the waves of 
the sea ? The hope of complete enumeration is the justifi- 
cation of counting.' 

Then why do we count the years and centuries? Do 
we pretend to know that they will have a numerable 
sum ? and when they have reached it, do we imagine 
that the race will survive to take an interest in the com- 
pleted enumeration? In the first place, for each of us 
time seems to have an end ; and in the second place, all 
history is parcelled out in overlapping epochs which we 
have an interest in measuring. We do not in fact ordina- 
rily know or compute the whole numerable series of years 
that has elapsed since the first events of ascertainable date 
in history; we adopt this or that era according to some 
overpowering historical interest which makes it seem to 
mark a fresh beginning. We do not count the years to 
ascertain their total quantity, but to give them names by 

chap, iv.] An 'infinite series! 177 

which we can fix events ; and as a means to fixing the 
relations of events we no doubt desire to note the quantita- 
tive relations within the total of historical time which has 
elapsed down to any given present. If we are pressed 
further, and told, ' But, after all, the years may go on for 
ever and the human race may go on counting them for 
ever,' we can only reply that the faculties with which we 
are endowed refuse to express this ' ever,' that at any point 
taken in the series we should be at some finite number, and 
that if a conviction of the endlessness of the series could be 
miraculously impressed upon our minds we could only 
conclude that, except as a record of the past, counting the 
years was an unmeaning form, seeing that the nature of the 
series could not be represented in number. A very simple 
case of enumeration ad infinitum would be that in which, 
by persistent errors of identification, we should count the 
same objects over again, round and round, without being 
aware that we were doing so. In such a case it is obvious 
that the conception of number would be destroyed so far as 
these objects themselves were concerned, though if they 
were at known intervals of space we might none the less 
use them as a measure for other things. When we measure 
with a foot-rule we do in fact count the inches marked on it 
over and over again in this way, not for their own sake or. 
the process would be infinite, but only for the sake of some 
other quantity which we characterise by them. In this 
respect the inch-marks on the foot-rule correspond to the 
physical changes which indicate the day and year, and 
which serve as a measure for occurrences other than 

An infinite series, then, is not anything which we can 
represent in the form of number, and therefore cannot be, 
qua infinite series, a fact in our world. Relations may 
indeed be given as actual which only an infinite series could 
represent on their quantitative side, such as the ratio of the 
diameter to the circumference of a circle. But for this very 
reason they never are adequately represented on that 

VOL. I. N 

178 Abstract Quantity. [Booki. 

side, although we may know and argue from the positive 
character of the series, which ex hypothesi its prolongation 
to infinity is not to change. Our constructive judgment 
requires parts and a whole to give it meaning. Parts 
unrelated to any whole cannot be judged real by our 
thought. Their significance is gone, and they are parts 
of nothing. 

Thus it is nonsense to speak of any definite number, say 
100, as a portion of number, in the sense in which a foot is 
a portion of a yard, or a minute of an hour. The question 
'what portion?' at once disposes of any such relation. 
Number as such cannot be identified with any particular 
total such that a given number is a definite fraction of it. 

Closely allied to infinite number, and in a great measure 

depending upon it, are the conceptions of abstract or ideal 

time, and of abstract or ideal space, tending respectively to 

generate ideas of infinite time and of infinite space. 

Abstract l n speaking of Comparison we saw that every ' now ' 

and Infinite , , * , . , , , , , , 

Time. tends to become a part within now and ' then, and every 
1 then ' again within ' then ' and ' then.' This analysis is very 
gradually brought about, speaking historically, in the evolu- 
tion of the tense-system. The sense of Time is in the first 
instance the mere consciousness of continuity in succes- 
sion, that is, the mere perception of a succession or pro- 
cess of change. This sense however being only possible 
through setting off the succession against a comparatively 
permanent background of consciousness, is in embryo the 
comparison of successions, with the development of which 
comparison measurement of Time, and with this the abstract 
idea of Time, are brought into existence. The measurement 
of Time consists in the equation of one set of perceptible 
changes identified by a common nature, to another set of 
perceptible changes, in the sense that the beginning and end 
of a numbered series of the one coincide with the beginning 
and end of a numbered series of the other. The enumera- 
tion of phases of one series that coincide with one or more 
phases of the other series might conceivably be undertaken 

chap, iv.] What is unvarying Duration ? 1 79 

apart from any belief that either series has a constant dura- 
tion in time, i. e. if repeated, would occupy the same 
amount of duration as before ; but in enquiring whether 
such a belief actually exists we must distinguish between the 
reasonable doubt whether any portion of any series ever can 
or will be repeated absolutely without physical modifica- 
tions which may affect its duration, and the unmeaning 
doubt whether a series assumed to be repeated without 
physical or causal variation may not nevertheless have 
varied in the absolute amount of duration which it occupied. 
The former kind of doubt will only lead to a demand for 
criticism and reciprocal adjustment of our time-measures, 
together with the temperate scepticism which our lack of 
exhaustive knowledge must produce about our acquaintance 
with even those natural conditions which we have most fully 
investigated. The latter kind of doubt, if pressed to its con- 
clusion, would reduce the enumeration of successive changes 
to a statement of mere numerical fact wholly devoid of signifi- 
cance. Such enumeration would not be impossible, but 
would scarcely fulfil the requirements of judgment. It 
would be on a level with the mere repetition of the names 
of numbers. It is hardly necessary to give instances ; 
every one can see at once that if we entertain the idea of 
variation in the measures of time occurring without any 
reason, all equation of successions becomes futile, and ceases 
to afford any ground of expectation or of inference. 

But though a doubt of this nature has been mentioned 
by great writers, yet it has never been extended to affect the 
only element of our time-perception which is essential to its 
utility, viz. the constant ratio obtaining between the succes- 
sions employed as measures of duration. This limitation of 
the doubt arises from the confusion in which it originates, 
the confusion which consists in treating the whole as if it 
were a part. Time, for us, is a relation, a ratio, and its 
constancy is the constancy of this ratio. If all processes in 
time maintain a constant ratio to one another so far as they 
are unaffected by physical modifications, then there is no 

N % 

180 Abstract Quantity, [booki. 

meaning in suggesting that tried by some unknown or im- 
possible standard x they may be variable. But yet this 
suggestion is a natural suggestion arising out of a natural 
confusion. We naturally frame an idea of duration in 
itself, as that which has successive parts really and abso- 
lutely equal, because equality of successive parts in terms 
of one of our time-measures is what we are always endeav- 
ouring to ascertain from some other time-measure. And 
we forget that equality, if we exclude from it the idea of 
measurement, ceases to be an intelligible conception. This 
ideal of duration then, whose successive parts, though ex 
hypothesi not measurable, are assumed to be equal, we 
actually set up as an imaginary measure against the totality 
of consenting measures and processes the ratio of which 
to one another forms our world of time, and is merely 
represented in an abstract and ideal form by ' duration in 
itself.' ' Duration in itself,' says ' Locke V is to be con- 
sidered as going on in one constant, equal, uniform course. 
But none of the measures which we make use of can be 
known to do so ; nor can it be assumed that their assigned 
parts or periods are equal in duration one to another.' 

But 'duration in itself not being a relation of successions, 
could not be perceived as time, nor could any being that 
perceives as we perceive be aware of equality or the 
opposite in its successive parts ; for equation is necessary to 
equality. If, on the other hand, we set it against our time- 
measures, then it becomes one measure among many, and 
in case of a discrepancy that should remain unaccountable it 
is only caprice that could choose which we should regard as 
right. The question in fact would be unmeaning, for the 
whole discussion obviously originates in the attempt to 
transfer an attribute which depends on a comparison to a 
set of terms considered in themselves and apart from com- 
parison, and then to suggest a comparison between them 

1 E. g. by measurement of successive phases against each other, which is 
Uf hypothesi impossible. 

2 Essay, book II. 14. 21. 

chap, iv.] 'Duration- and ' Thing-in-itself! 18 r 

(the supposed equal parts of ideal duration) and the totality 
of our time-measures of whose reciprocal relations those 
parts are an idealised form. 

But this confusion does not naturally originate a doubt 
of the constant ratio, physical disturbances being allowed 
for, of our measures of time compared with one another. 
For it is this constant ratio from which the idea of duration 
as such, hypostasised by abstraction into duration in itself 
with equal successive parts, is derived ; and to doubt the 
constancy of this ratio would be to deprive ourselves of 
that idea of duration on which the confusion itself depends. 
If oscillations of a pendulum of fixed length, such as are 
normally equal when measured by the rotation of the earth, 
may vary without a physical cause affecting either of the 
compared motions, the conception of uniform duration is 
destroyed, and no equation of successions is more than 
an isolated fact. On such a hypothesis there would be 
nothing to generate the idea of uniform duration, and no 
measure of time with which to compare that idea. 

The antithesis between duration in itself and our measures 
of it is merely a case of the antithesis between the thing-in- 
itself and our knowledge of it. It is possible, though un- 
meaning, to doubt whether our knowledge as a whole is 
real knowledge i. e. corresponds to some test or condition 
which we may imagine as imposed upon it from without. 
The possibility arises from our possession of an ideal of 
knowledge, which by an act of abstraction can be set in 
antithesis to the actual whole of knowledge from which it is 
abstracted. But it is impossible when operating in detail 
upon the matter of experience to doubt the existence of 
rational connection in any one particular group of appear- 
ances ; for by so doing we paralyse the understanding, 
which can only act in the search for causes, and leave 
neither knowledge to condemn nor an ideal by which to 
condemn it. We shall have to return to this subject in a later 
chapter, when we speak of the postulates of knowledge. 

We have just seen that it is idle to treat the whole as if 

1 82 Abstract Quantity. [booki. 

it were a part our reciprocally adjusted measures of time 
as if they were one measure among many. It is also worth 
while to observe in the same instance the impossibility of 
making a part do duty for the whole, which is strikingly 
exemplified in the ultimate data of time. No process of 
perceptible change is a trustworthy measure of time except 
in as far as it is equated with other processes of known con- 
stancy, and observed to be in itself free from physical 
causes of variation. That is to say, the part can only be 
taken as a definite standard when it has been criticised in 
the light of the whole. This is true of all premises of 

Amount of Time, like all quantity, is measured by the 
enumeration of units which have a known value. But, 
unlike any other kind of quantity with the exception of 
space, it follows number not only into mediate counting 
(all quantity does this), but into enumeration ad infinitum. 

Simple enumeration in the case of Time gives such judg- 
ments as \ He died three years ago,' ' It is seven days since 
I saw him,' which expand by reference to a standard of 
succession the mere indications probably of various nature 
and origin 1 conveyed by the tenses. 

Mediate or complex counting in Time gives such judg- 
ments as the equation ' 365 days = one year.' Such judg- 
ments deal with our real and ideal time as the result gained 
by comparison and equation of actual processes in expe- 
rience. But the abstraction which stands as subject tends 
to assert itself as a something apart from the actual pro- 
cesses whose relation it is, and thus as we have seen 
generates the conception of ' duration in itself ' or ' absolute 
time,' which again having lost the element of totality pre- 
cipitates us into the idea of infinite time. 

Enumeration to infinity, when applied to the parts of 
time, has characteristics analogous to those of infinite 

1 Tense need not have originated in the idea of succession at all ; and may 
often have arisen out of the expression of emotions or anticipations or out of 
the mere negation of presence as a perception of a certain kind. 

chap, iv.] Reality of World in Time. 183 

number, but more striking, inasmuch as time is closely- 
bound up with the attributes of actual existence. Infinite J 
time is, like infinite number, an unending whole, which is a 
contradiction in terms. That is to say, we are prevented 
by the nature of our minds, if by no other cause, from 
attaching any meaning to infinite time as a quantitative 
expression indicating an aggregate expressible by enumera- 
tive judgments. Whether the problem (for so we must 
consider it) which is put before us in this form is capable of 
becoming, not a problem, but a fact, in some other form, is a 
question which does not concern us here. The instances 
which are alleged to show that an infinite series may be 
given point somewhat in this direction ; I allude to such an 
instance as that of the relation between diameter and cir- 
cumference. However this may be, it remains true that 
infinite time, as a mere quantity of duration, is a phantom 
generated by a meaningless abstraction. 

But, as we asked whether there may not be endless 
numerable units, so we may be challenged to ask, May- 
there not or must there not have been an endless chain of 
actual occurrences in succession ? And if we are prepared 
to deny reality to every endless series, must we not first of 
all deny it to the actual world as in time, and we may add 
by anticipation of the next section, as in space ? There can 
be no doubt that the relativity of events and appearances 
in time and space does involve for our minds an infinite 
progression in the way of referring one thing or appearance 
to another as its cause or explanation, or at least as in some 
way its determinant. We can hardly conceive that we are 
really counting in a circle, but our position is just as hope- 
less as if we were. Our ideas of reference, determination, 
causation, do not allow us to fancy a first event, a beginning 
of time, or a limit of space. On the other hand, so far as 
we can understand, it is impossible for such a succession as 
we postulate to be actual in the sense in which a known 
section of history is actual. It is not merely something 
more than we do construct as a whole ; it is something the 

184 Abstract Quantity. [booki. 

essence of which is to be incapable of construction as a 
whole. We may say if we like that we are bound to think 
of such a succession as actual in the sense that it is a 
problem inseparable from the relativity of our world ; but 
we cannot take the endless series qua endless as a positive 
element in our organised experience. 

In dealing however with the succession of actual events 
having positive character and content we are in spite of 
their serial appearance on different ground from that of 
abstract time or equable succession as such. Actual 
events the history of our world have more in them 
than a mere series. We may say either that the world 
in time and space is not mere succession and externality, 
or that the real world which intelligent perception pre- 
sents to us is not merely a world in time and space. 
The human mind and will are always busy in turning a 
series into a coherent and almost individual whole, projected 
more or less definitely on a scene of time and space, but not 
exhausted in its meaning by the nature of that background. 
Greece for instance or England are not mere 'geogra- 
phical expressions ; ' and if they were they would still have 
a physical unity of a deeper kind than the juxtaposition of 
extended units or the sequence of a series. They are 
historical realities, but their coherence lies in their meaning. 
Therefore in denying that for us, in our way of under- 
standing, an endless progress can be a real and controlling 
factor of organised experience, we do not deny the reality of 
the phenomenal world as presented to intelligent perception. 
Abstract , The nature of Space is in many respects analogous 

andlnfinite ' r . ,, , , / /., , . s 

Space. to that of time, and bears on the whole a similar relation to 
the system of number, with its degrees of simple or 
categorical counting, mediate or complex counting, and 
counting ad infinitum. The corresponding grades of ab- 
straction in dealing with space may be identified as 

a. The measurement of actual distances. 

b. The theoretical relations of spatial qualities, including 
the whole of the mathematical sciences, excepting what may 

chap, iv.] A dual Distances. 185 

be included in the mere system of number, viz. all forms 
of simple and generalised (algebraical) arithmetic ; and 

c. The conception of infinite space. 

In defence of the subdivision here adopted, I venture 
with a good deal of diffidence to suggest that the idea of 
infinite space is not an idea belonging to geometrical 
science. The employment of the idea of infinity in 
geometrical reasoning belongs, if the account above given 
of it is correct, to the second of the above heads, being 
really an abstract mode of describing a geometrical whole. 
If enough space is given to make manifest the positive 
nature of the whole before us, it would seem that no 
addition can really affect the case. Quantitative infinity 
may be a roundabout description of a direction or a quality. 
That a certain straight line is infinite may only mean that 
its direction is such that it can never meet a certain other 
straight line. 

a. The measurement of actual distances is prima facie a Measure- 
case of simple measurement, and must obviously arise at ^ai 
the point where positions distinguished by the comparative distances, 
judgment are discovered to have relations of distance and 
direction reducible to degree. Degrees of distance from 
assigned points, and proportions of such degrees, considered 
as properties of objects, pass into the determination of con- 
crete individuals and of their characteristic attributes. In 
this respect we have considered them above. But also, 
receiving their significance from a system of equations by 
which all spatial magnitudes are brought to a common 
denomination, they contribute to reflection upon space 
in the abstract, a reflection which is developed by the 
process of enumeration applied to the parts of space when 
thus idealised and considered for their own sake. The 
system of measures, as we have seen above, is a connecting 
link between simple and complex measurement. It is 
prima facie a. system of ratios, and requires an arbitrary 
starting-point to give it meaning. But when taken as 
general and typical it passes into a system of proportions, 

1 86 Abstract Quantity. [booki. 

as we see in such a judgment as ' This map is on the scale 
of twelve inches to the mile.' There need not be twelve 
inches in any direction in the actual mapbefore us; the phrase 
expresses a proportion, not a simple fact of enumeration. 
It is not necessary to know, for the purpose of the scale, 
how much absolutely (i. e. in the mass of other relations) 
an inch or a mile is ; we can interpret the scale if we know 
how many inches there are in a mile. The abstract 
numerical expression I : 63360, which is a proportion 
as governing the relation between every part of the map 
and the corresponding part of reality, represents what the 
formula ' one inch to the mile ' really means to say. We may 
compare this case with the financial expression 'five per 
cent.'; some newspapers will print this as $ per cent., 
which is a confusion between singular or merely actual, and 
generalised or proportional ratio. They do not really 
mean that $ need be concerned ; their predication is as 
true if the interest in question only amounts to five shillings. 
The expression five per cent, is simply a fractional or pro- 
portional expression. 

Now, when, e. g. in the two instances just quoted, the 
reference to an arbitrary magnitude is dropped out, and 
when moreover the generalised equation is taken as ex- 
pressing the relations between distances in space com- 
bined in a certain way, then we have ideal or mediate 
enumeration as it exists in geometrical science. ' Mediate ' 
because the proportion contained in the equation is af- 
firmed of reality as qualified by definite spatial attributes, 
which therefore enter into the content of the equation as 
interrelated conditions. The equation of an ellipse is a 
hypothetical judgment asserting that the axes of an ellipse 
(or other quantities involved in an ellipse) being treated in a 
certain way will be always equal to themselves treated in a 
certain other way. It is obvious that being mediate this 
geometrical enumeration or computation is also complex * ; 
for the conditions by which it is mediated may involve 
1 See p. 172 above. 

chap, iv.] Geometrical Equation. 1 8 7- 

units of any degree of numerical complexity. Thus judg- 
ments dealing with squares and cubes, still more with conic 
sections, presuppose, on their numerical side, more or less 
elaborate enumerative processess as involved in the forma- 
tion or apprehension of the spatial unit. 

b. The generalised relations of spatial attributes form a Geometry, 
systematic science with a distinctive object-matter. 

(1) 'Any two sides of a triangle are together greater than Indivi- 
the third side.' 'Triangles upon equal bases and between spatiS 
the same parallels are equal to each other.' ' The square of Figures. 
the hypotenuse is equal to the squares of the containing 
sides.' ' The angles at the base of an isosceles triangle are 
equal to one another.' 

Such judgments as these are among the simplest results 
of mediate enumeration 1 as applied to space, and they pre- 
sent an obvious peculiarity shared with them in a high 
degree by complex judgments of mere number, and in a 
less degree by judgments that compute time. Although 
geometrical science proper consists, as a science, exclusively 
of the equation with each other of variously described 
spatial units, which, if we further consider the sciences of 
motion, we must take as referred to units of time, yet under 
this ' variously described ' there lurks a whole classificatory 
science of forms possessed of structural unity and quasi- 
organic relations between part and whole. Thus in the 
definitions and definitory judgments of geometry, as in the 
inductive judgment of enumeration, there is a revival of 
that structural subordination of part to whole which, 
though dormant, yet is never dead so long as judgment has 
a meaning. The triangle, the square, the circle, the ellipse, 
though each of them capable of being exhaustively defined by 
generalised enumerative processes dealing with homogeneous 
units, have also an aspect of structural unity and subordina- 
tion of parts to the dominant quality of the whole. Both 
clauses of this statement are however subject to reservation. 

x For the further distinction between arithmetical and geometrical reasoning, 
see Bk. II. ch. 2. 

1 88 Abstract Quantity. [bookt. 

In the first clause, the expression c homogeneous units ' is 
not entirely adequate to the facts. Distances in the three 
spatial dimensions are indeed as distances homogeneous, 
but it can hardly be said that an angle is homogeneous 
with a distance or direction, although a proportion of dis- 
tances is an exhaustive measure of an angle. Therefore, 
though an angle may be represented in terms of distance, 
yet in considering the elements in the spatial structure 
of a square or triangle we must assume the angle as well as 
the straight line. The apprehension of converging direction 
is hardly given in the mere apprehension of direction. 

In the same clause we must qualify the assertion that all 
geometrical shapes can be exhaustively defined by equation 
of quantities. I presume that the impossibility of squaring 
the circle implies a difference of kind between circle and 
straight line which is disguised but not destroyed by the 
efficient methods employed to express the one in terms 
of the other 1 . Here again, in the adequacy, as distin- 
guished from exhaustiveness, with which quantitative equa- 
tions represent characteristics of kind not wholly reducible 
to quantity, we find an analogy with the various systems of 
necessity which are superimposed upon one another in the 
organic and moral worlds. 

And the truth of our second clause would be a good 
deal interfered with, if not annihilated, by enlarging our 
list of geometrical figures, and by regarding every figure in 
all its possible variations. As to the first point, every 
spatial figure is a geometrical figure ; and those which we 
mentioned, together with others that occur to the mind at 
once as commonly considered in plane and in solid 
geometry, have no real prerogative of existence to the 
exclusion of trapeziums or any other irregular figures, even 
if partly curved and partly rectilinear in outline. The 
world would be easier to explain than it is (or so it seems 
to a superficial glance) if irregularity, ugliness, and disease did 

1 The quadrature of the parabola shows that the impossibility of squaring 
the circle does not arise from the mere difference between curve and right line. 

chap, iv.] Continuity destroys Species? 189 

not, as they do, exist by law and necessity 1 just as much as 
symmetry, beauty, and health. It may be said in defence 
of treating the regular figures as if there were no others, 
that all others are reducible to them, all rectilineal figures 
to triangles, and so on. But this is a mere ideal reduction 
by measurement, and in no sense a deduction of the exist- 
ence of the one from that of the other. 

And again, most ' figures ' of which we speak are really 
classes of figures, even if we take all ' similar ' figures as the 
same, i. e. disregard size and only look to characteristic pro- 
portion. I do not know why we should not take the conic 
section as ' a figure ' and treat the circle simply as a case of 
it. Anyhow the ellipse comprises in itself a whole class of 
figures which are qualitatively quite different from each 
other, and pass by imperceptible gradations into figures 
which are not elliptical. By insisting on facts like these 
we might melt away the individuality of typical figures, 
and exhibit every group of geometrical shapes as destitute 
of common characteristics beyond those which flow from 
the mere genetic relation itself. Thus, for instance, an 
ellipse when just passing into a circle or into a straight 
line has none of the characteristics which we associate with 
elliptical form, although the analytic relation by which its 
nature is theoretically determined may be within the limits 
which must as a matter of geometrical classification be 
assigned to that figure. Such a treatment would be the 
triumph of explanatory theory and necessary connection 
over individuality and characteristic quality. But it is a 
treatment of which, in geometry, the facts admit, and which 
even in the organic world is rendered indispensable by the 
idea of continuous evolution. 

It is right that attention should be drawn to the above 
reservation. No habit is more pernicious than that of 
assuming what is obvious and familiar in a certain sphere 

1 I do not say by the same necessity ; I only mean that they result mechani- 
cally from natural conditions. Any limitation of which this statement may be 
capable must refer to a distinction of kinds of necessity. 

i go Abstract Quantity. [booki. 

to exhaust the contents of that sphere. Every figure is 
geometrical ; and even if all irregular figures can be reduced 
for purposes of reckoning to the more regular types, this 
does not justify us in speaking theoretically as though there 
were no figures in space besides those which have been 
selected as typical by geometricians. 

We must meet such conceptions now as we shall 
have to meet them again, perhaps more than once, in the 
evolution of the judgment, by the reflection that one 
positive existence cannot, by the mere fact of its existence, 
cancel another. There may be non-elliptical ellipses, 
figures which fulfil one set of conditions that mark the 
ellipse, but lack attributes without which we hardly recog- 
nise the figure ; and there may in the same sense be or 
have been (time makes no difference) non-human human 
beings. And explanatory theory may be able in both 
cases to trace step by step without saltus or miracle the 
transition from the one phase into the other by develop- 
ment of elements fundamental in both. But this will not 
obscure our perception of the elliptical shape of a character- 
istic ellipse, or of the humanity of a typical human being. 
The typical human being is made typical, as we shall 
see, by real teleology. The typical ellipse is only typical 
through a subjective quasi-teleology. This is the differ- 
ence between the two cases. 

Thus, in spite of the above reservations, it remains true 
that in complex enumeration as applied to Space the 
antithesis of individuality and necessity is strikingly illus- 
trated. A generalised relation of distances, not obviously 
differing in kind from any other generalised enumerative 
relation, when interpreted into an actual figure, may at 
least produce a structural totality complete in itself and of 
a marked individual character. It is enough to mention 
such simple instances as the equilateral triangle, the square, 
and the circle. These totalities do not refer outside them- 
selves for definition in the obvious sense in which simple 
magnitudes are forced to do so. They are primarily cases 

Chap. iv. ] Is Geometry ca tegorica It 191 

of internal proportion, of proportion, that is, between one 
and another element of a single totality. Relativity appears 
in them in another shape than that of simple equation with 
absolute (in the sense of arbitrary) standards of magnitude. 
A particular triangle or ellipse is relative and finite chiefly 
in the sense of being derived from arbitrary conditions, no one 
value of which has any prerogative of existence as against 
any other, and an extreme modification of which will always 
destroy the essence of the figure. There is also a further 
sense in which all natural existences are finite as compared 
with mind, because they cannot refer to themselves, but only 
are to themselves or to external conditions. 

The subordinate totalities of Time, such as the hour, day, 
and year, are not really cases of the same principle, for 
they are mere aggregates of units without a limiting 
totality, and are simply formed by arresting enumeration 
at intervals prescribed by external interests. A better 
parallel may be found in the numbers of the numerical 
series which are distinguished by any peculiarity, e. g. prime 
numbers, squares, cubes, etc., if we consider these peculiar 
cases in their relation to the one unvarying process of adding 
together homogeneous units. This simple synthesis of num- 
ber may be regarded as analogous to the mechanical or 
necessary aspect of an individual thing or figure, and its 
peculiarity as square or cube to structural totality. 

(%) Figures in space then, and numerical relations, al- Exist- 
though abstract and ideal, and arbitrarily selected out of Jjjj^ s in 
continuous sets of value of which no one has existence by Space, 
preference to the other, yet seem capable in a sense of 
possessing characteristic quality and self-sufficing totality. 
What is to be thought of their existence ? Do such judg- 
ments as are mentioned on p. 187 involve the assertion 
that the qualifications of Reality which form their subjects 
are actual, and if so, in what sense are they actual ? The 
difficulty of the question is only displayed in its true 
extent if we add to the above instances some ideas for which 
actual existence, as diagrams in books or as thoughts in the 

192 Abstract Quantity, [booki. 

minds of individual students, cannot with probability be 
claimed ; e. g. the idea of a polygon with a thousand and 
one equal sides, of any trapezium chosen at will, or of 
any irregular figure or high number. 

It is clear that the square or triangle qua spatial figure 
has no actuality which does not equally belong to all such 
less familiar shapes, and therefore mere presence in the 
individual mind is not the existence in question. And 
indeed to speak of it as such would be to enter upon a 
vicious circle which would stultify the judgment ; for it is 
essential to the judgment to affirm a reality outside itself, 
and it would be too ridiculous that your judgment should 
refer merely to the content of mine as the reality asserted, 
and mine in turn to that of yours. It is obvious that the 
two manifestations of the thought-function are on a level, 
and if each refers to the other, each might just as well 
refer to itself, i. e. find its truth in the simple fact that it is 
made 1 . A triangle must be just as real when no one is 
thinking about it as when many students are engaged upon 
the conception of one. This is of course not the same as 
to say that spatial figures do not depend on the spatial 
consciousness, or on consciousness at all. We are only 
saying that they cannot depend for actuality on one par- 
ticular reflective consciousness of those particular figures. 
The world as it is for perception and intelligence is the 
object-matter of our whole enquiry, and we have no occasion 
to raise a question that assumes the destruction of the 
object which we are considering. 

The absence of material existence and also of any mode 
whatever of particularisation in determinate forms (the 
selection e.g. of a typical ellipse not being justifiable 
on purely geometrical grounds) must however make a 
distinction between the actuality of the contents under 
discussion and that of material things or their sensible 

1 Reference to the world of meanings or objective reference (Introduction, 
sect. 7) is not merely reference to judgments in fact made by others. It is an 
inadequately conditioned reference to reality. 

chap. iv. j Are spatial figures real? 193 

properties. Admitting, as we must admit for logical 
purposes, that Space is to be reckoned with as having 
a peculiar actuality of its own, still it is not clear in 
what relation geometrical figures, apart from the shapes 
of actual objects, stand to actual space. Geometrical 
figures as such, the subjects of judgment in geometrical 
science, are not the shapes of actual objects ; they are 
not identical with any perceptible figure ; they are not 
distributed through space nor present as special charac- 
teristics in any portion of it. I do not know how to \f 
describe them better than as a peculiar class of laws 
or attributes of the spatial relation as such, which are 
concrete in the nature of their content, though abstract 
in their medium of presentation. And in the same way 
the characteristic totalities of number must be taken as 
laws embodied laws of the enumerative relation of part 
and whole. 

We may illustrate the nature of such attributes by 
comparing them with any purely imaginary ideal content 
which bears (so far as an imaginary content can, for it 
is always, in my opinion, found wanting somewhere) 
the character of self-sufficing totality. Such an ideal 
content for instance is Shakespeare's Hamlet 1 , or the 
material spheres of ancient astronomy, or, to come nearer 
to our present subject, the conception of ' Flatland ' as 
space in two dimensions only, with sentient beings confined 
to it. These conceptions, though doubtless based on 
elements of fact and illustrative of real conditions, yet 
exist only in the minds of those who read and think about 
them, or more strictly in the identical reference which 
these minds are stimulated to make to a world of meanings, 
but a world of meanings explicitly discontinuous with and 
detached from the actual world of fact, or what we call in 
short an imaginary world. Such a world is indeed main- 
tained by judgment, but it is judgment of a peculiar kind 

1 Omitting the considerations which arise out of the artistic truth of the con- 
ception, and taking it merely as an illustration of an imaginary idea. 
VOL. I. O 

194 Abstract Quantity, [Booki. 

and under peculiar conditions subject, not like the common 
world of meanings to a wholly indeterminate, but to a 
conscious and explicit, abstraction from reality, which be- 
comes semi-conscious in artistic fiction, and utterly lost 
and obliterated in mere error and superstition. 

The figures which represent the properties of actual 
space are not imaginary in this extreme sense of the word. 
It might however be a question whether the difference 
between them and such ideas as have been mentioned 
is one of kind or one of degree. Both kinds of ideas it 
might be said involve abstraction from concrete perceived 
reality, both kinds are therefore hypothetical and not 
actual existences, and how far the abstraction is carried 
cannot be a question of principle. Nor, I must add, do I 
mean to insist on the manifest contradiction with experience, 
or self-contradiction when viewed in the light of experience, 
that some of my instances of imaginary ideas may be held 
to present. The distinction which I desire to draw is 
simply between abstract but real, and purely imaginary 
contents, when employed as subjects in judgment. 

Perhaps the distinction might be found as above suggested 
to consist formally in the nature o{ the abstraction to which the 
two kinds of contents are severally subject. A merely abstract 
content is subject only to the abstraction which its ostensible 
nature implies. The name of a figure in space is the 
name of a figure in space and not the name of a man or 
a mineral or of any material object. But the name of 
Hamlet for instance is and yet is not the name of a man. 
The name of a knot tied on an endless string is and yet is 
not the name of a reality in space. These imaginations are 
subject not merely to the abstraction which separates every 
content from all that is not included in it, but to a further 
abstraction which says, ' This is a meaning, but not the 
meaning you would take it for : ' in other words, it is con- 
ditional within a world which itself can only be predicated 
conditionally and not directly of the reality with which we 
are in contact by means of perception. 

chap, iv.] Generic and Quasi-generic. 195 

Thus we may say, if we choose, that our ideas of actual \l 
space have for their meaning only possibilities, but these 
are at least real possibilities, that is to say, their funda- 
mental generating relations actually exist in the world 
which centres in present perception. They are therefore 
as real as colour in the dark or as sweetness which we do 
not taste. And if we pronounce these attributes unreal 
outside the moment of perception, we have laid the axe to 
the root of the perceptible world. We might as well say 
that the wall in front of me is actual and that behind me is 
not. But what corresponds with these ideas to the actuality 
which colour and taste do partake of when perceived ? Here 
we find a real difference. Such actuality in sensuous pre- 
sentation they cannot have. But we do not of course admit 
that Reality is restricted to sensuous presentation. All we 
can say is that in all relations of actual things these spatial 
attributes make themselves evident as controlling conditions, 
and are introduced as conceptions without which the mind 
fails to construe the phenomena. They are abstract cha- 
racteristics of the actual spatial relations of things, and are 
as much a fact for logic as any secondary quality, qua 
general quality; and they are not on a level with mere 
imaginations and fictions, even if these are consistent, or 
not notoriously inconsistent, with reality. 

(3) The judgments mentioned on p. 187 are thus found The quasi- 
to display in their own line of abstract evolution which we judgment. 
are now pursuing a character analogous mutatis mtitandis 
to that which the Generic Judgment will be found to display 
in the concrete evolution of thought. The subject of each V 
such judgment is Reality qualified as a structural whole 
which embodies properties rooted in an actual relation and 
controlling the consequences of that relation at every turn. 
The figures in question do not claim sensuous particularity v 
and are not capable of it. The judgment therefore is a v 
degree less generic and more hypothetical than classificatory 
judgments which retain much of the meaning of the col- 
lective judgment. 

O % 

196 Abstract Quantity. [booki. 

Yet the judgment in question is generic. In the first 
place, the particular figures which arise if particular con- 
ditions are assumed are individual totalities, not indeed 
having sensuous singleness, but self-identical as laws of 
space. And in the second place, although no doubt any 
series of such figures (triangles, ellipses, etc.) is in one point 
of view an infinite series (the transition from value to value 
of the generating conditions being absolutely continuous), 
yet the whole falls within known limits, and is bound to- 
gether by a characteristic quality which might probably be 
found to vary with the variations of the generating factors \ 

Therefore a judgment like this presupposes, not as do 
the judgment of zoology a limited even if very large number 
of actual individuals forming a real historical unity though 
spoken of mediately and by help of an abstract qualification 
of Reality, but a series of laws regulative of form, or rather 
a law expressed in a series of forms, having positive common 
characteristics and bounded by definable limits within which 
the whole series must fall. 'All triangles ' is hindered from 
meaning every particular triangle (i.e. variety of triangle 
I abstract from particular sensuous presentations all 
through this discussion) not only as ' all men ' is hindered 
from meaning every particular man, by the practical im- 
possibility of dealing with such a meaning, but also by a 
theoretical absurdity, for all particular triangles would be 
an infinite series, which need not theoretically be the case 
with all particular men. But, as we saw above, a series 
which has a known positive character or falls within known 
limits may be treated as an actual unity in spite of its 
infinity. ' All triangles have their angles equal to two right 
angles' is a judgment about what is really a single con- 
tinuous relation, but embodied to the mind's eye in certain 

1 It seems obvious that as one generating factor, e. g. one axis of an ellipse, 
approaches disappearance, we should expect the characteristic quality to diminish. 
But any such conception is not easy to carry out. E. g. if we take equality of 
the axes as the characteristic point in a figure of the conic section class, we get 
the circle as the characteristic type to the exclusion of the ellipse. The question 
has perhaps only an aesthetic interest. 

Chap. iv.] Subjectivity of Sense-forms \ 197 

salient types resulting from geometrical classification. It 
resembles the generic judgment more strikingly than 
appears at first sight, for the generic judgment too deals 
with a section of evolution in which a vast though not 
infinite array of transitional types has really bridged the 
gulf between the marked species which are familiar. 

c. Infinite enumeration applied to the parts of space is infinite 
the last result of abstraction in this region. Here, as in space " 
time and number, we have the idea of the absolutely homo- 
geneous part, i. e. the part whose repetition has no tendency 
to generate a whole. The idea of infinite space is the idea 
of the endless synthesis of such parts, which must always 
present to us the appearance of an unsolved problem. If 
the problem has a solution, it must consist in changing the 
point of view from which we regard it, as if, to repeat an 
illustration which I employed above, we were suddenly to 
awake to the fact that we had been counting parts extended 
in a circle and not in a straight line. 

Will not the doctrine known as the subjectivity of space 
and time help us to explain the nature of this contradictory 
reality? Up to a certain point it has undoubtedly done 
good service by showing that the difficulties which attach 
to sensuous reality are rooted in the nature of the percipient 
intelligence itself, and must be reckoned with as inherent in 
sensuous experience. But I am unable to see that the 
'subjectivity' of these forms of apprehension can carry us 
further, unless or until we are enabled to put something 
better in their place. At present we seem only to have learnt 
that the difficulties of knowledge are not external to it, but 
are inbred and inevitable, at least so far as concerns the 
series of sensuous phenomena. But we gain nothing, so 
far as I can understand, by attempting to erect a world 
beyond as a non-sensuous counterpart of the sensuous 
series. If a counterpart, then it would seem to share the 
difficulties attaching to this series, while as non-sensuous it 
lacks the compulsory reality of sense-perception 1 . Our 

1 Lotze has well brought out the difficulties attaching to the conception of 

198 Abstract Quantity, (Booki. 

present knowledge rather points to the conclusion that if 
we are to attain something less contradictory, more capable 
of self-sufficing reality, or if we like to use the phrase, more 
above sense, we must look for it in facts and purposes which 
deepen the significance of life, not in a shadowy counterpart 
which repeats the world of sense without enhancing its 
value. Mere series, mere space and time, we must always 
remark are mere abstractions ; and though no human know- 
ledge is free from relativity, i. e. from the reference to what 
falls outside it ; yet on the other hand no actual human 
knowledge is, like the abstract infinities, mere relativity and 
nothing more. There would be some justification for saying 
that, as contrasted with the concrete structure of individual 
things, a 'subjective,' i.e. artificial and unreal, character 
might be attributed to number, space and time as infinite 
wholes ; on the ground that they conflict with the nature of 
actual fact however comprehensive, and that the extension 
to infinity deprives them of relation to the phenomena in 
which they are known to us. But the distinction is hardly 
sound, for it is at best one of degree. The difficulties of 
relativity do not wholly cease as soon as we turn away 
from the abstract infinity of mere number, time, and space ; 
in common ideas of causation they affect the actual content 
of phenomena. From the very beginning of knowledge, as 
I have tried to point out, Absoluteness co-exists with Rela- 
tivity; but it is impossible to form categorical judgments 
of a comprehensive type until the idea of causation has been 
freed from its primary implication of an endless series. 

The question might be asked, why are we exclusively 
tempted to demand the reality of infinite time and infinite 
space when there are other abstract conceptions of homo- 
geneous parts not subordinate to any whole, which might 
in the same way be pushed to infinity? In the first place, 
it may be replied that abstractions of this class are not so 
common as might appear. The essence of them is that 

an ' intelligible ' counterpart to the world of sense. The strange thing is that 
they do not appear in any way to make him discontented with that conception. 

Chap, iv.] Space and Time why so importunate. t 99 

progressive enumeration shall not tend to modify their 
character. Thus intensive quantities, such as infinite force, 
infinite velocity, are conceptions of a heightening the later 
stages of which would modify the earlier and not remain in- 
differently beside them. Therefore although the phenomena 
of velocity or of force do suggest the idea of quantitative 
infinities of those kinds, yet they do not impel us to judge 
those infinities to be real, because the perceived forces do 
not in their nature refer to and presuppose infinite degrees 
of themselves, but rather each manifestation per se excludes 
the infinity which would involve a qualitative change in 
itself. Infinite force or velocity is as contradictory an 
idea as infinite space, but is not in the same sense a 
problem or a paradox, because it does not in the same 
sense claim reality. 

And secondly, Space and Time may be called the 
Categories of sense. That is to say, they are the only 
principles according to which the world of sense-perception, 
both of our own immediate feelings and of external objects, 
appear to us to be possible. The question is not merely 
whether we can imagine the absence of either or both. I 
take it that experience would reply to this by saying that 
we cannot seriously imagine (i. e. conceive with full considera- 
tion) the absence of either in a world of sense-perception \ 

But the real point is not merely psychological, although 
of course in dealing with it we must appeal to facts of the 
mind. The point is that the very character and essence of 
sense is isolation, and therefore in apprehending variety, 
series. So extreme is this character of isolation that the 
presentation of sensuous contents even as a series is due to 
an intelligence that goes beyond sense. Space and Time 

1 Psychologically speaking, I should suppose that we may lose consciousness 
of either, perhaps more readily of space, e. g. when listening to music. Time 
is perhaps the more importunate of the two ideas because it extends to our inner 
feelings, etc., and I suspect this to be the reason of Lotze's notion that time 
is more ' objective ' than space. Yet we may of course in a fit of absorption lose 
consciousness of time. I do not suppose that these half-illusory states are at 
all perfect in their neglect of the non-obtruding element. 

200 Abstract Quantity, [Booki. 

are for us the first work of knowledge, as the conquest of 
them is the second. But all we are concerned with here is 
that, assuming the impulse to construct out of our sensuous 
perception a whole of the same nature as itself, we cannot 
but attempt to erect space and time also into wholes, an 
attempt which is frustrated as we have seen. 
Mechanical Hi. But, lastly, reflective science in pursuing an analogous 
Universe, attempt does meet with analogous difficulties. It assumes 
as further characteristics of the sensible world the abstrac- 
tions of matter and motion. Matter and motion are the 
abstractions in which the sensuous world is reduced to 
homogeneity in order to be susceptible of quantitative treat- 
ment, and in this treatment they are able to a large extent 
to represent genuine and actual relations of that world. In 
this respect they correspond to the structural classifications 
of geometry, and form the content of mechanical science. 
It would hardly be true I suppose to say that the infinity 
of matter and motion in space is an inevitable paradox to 
the scientific consciousness. It appears possible to conceive 
of the universe as a coexistent finite mechanical whole, 
demanding no determination from without. But this is only 
because the determination from without is thrown back in 
time by the doctrine of the eternity of motion, which, with 
a similar doctrine applied to matter, introduce the infinite 
series under the guarantee of the law of causation. Here 
again we have the insoluble problem which arises from the 
relativity of the sensuous world and presses upon us in its 
naked form as soon as, by reduction to homogeneity, the 
element of absoluteness or totality which helped to balance 
it is destroyed. It is to the latter element that we really 
look for a solution in the degree in which it is possible. 
The infinite series cannot itself be reality, but so far as we 
can transmute the series into an articulated whole, so far we 
can gain a reality out of it. 

This distinction suffices to justify the well-grounded con- 
clusions of science respecting the past and future of the 
material universe. Such conclusions are contributions to 

Chap, iv.] Concrete and Abstract Individuals. 201 

the projection that forms the actual world in which as 
percipient and intelligent beings we live. But with eternity 
in the shape of infinite regress and progress such a projec- 
tion can have nothing to do. 

We have thus traced to its climax in mechanical science 
that form of identity and difference in which an identity 
is regarded as the sum of the differences in which it is pre- 
sented. This one-sided aspect of identity and difference is 
what takes the shape of whole and part in the strict or 
quantitative meaning of those words, the meaning in which 
the whole is taken as equated to a relation, whether par- 
ticular or generalised, of homogeneous parts. 

It naturally occurs to us to ask at this point, how, if 
quantity is homogeneous, and if proportion is, as we have 
reckoned it to be, generically a quantitative relation, the 
concrete individual (vid. p. 135) whose characteristic quality 
takes the shape of proportion differs in content from a re- 
lation in number, figure in space, or system of motions 
which, though purely quantitative, is also, as we have 
seen, characteristic and self-contained. In the first place, 
we have spoken of the quasi-individuality which does attach 
to the structures that embody geometrical and, we may 
now add, mechanical laws. And we must remember that 
their quasi-individuality is only made possible by a 
certain revival of the qualitative element within the whole 
of quantity, even if the quality so present throughout the 
parts is, like the curvature of a circle, constant in all of 
them. And in the second place, we have to point out 
that in a true concrete individual its individuality exists 
in the form of a conscious purpose, a real teleology, and 
is the cause of its homogeneousness, the proof of this 
being that if the elements are isolated and removed from 
the individual they fall back into disparateness. The 
proportion in which its parts are held together is as we 
saw 1 secondary and not primary; it is a proportion be- 
tween proportions. And though it is true that in the 
1 See p. 139, above. 


Abstract Quantity. 

[Book T. 


simplest forms of comparison, such as matching a colour, 
judgment and equation are hardly to be distinguished, 
being in fact as yet in their common germ, yet the peculiar 
secondary unity of a complex whole characterised by in- 
ternal proportions is not fully expressed by reciprocal 
equation of its elements. Thus the concrete individual 
is from the first characterised by rather than equated to 
pure quantitative relations of parts. With abstract tota- 
lities just the reverse is the case. Their elements, homo- 
geneous to begin with, are placed arbitrarily in any whole 
(in as far as the elements of various curves resist such 
construction they are not pure quantity), and only acquire 
the semblance of a relation to a whole by their non- 
resistance in such a construction ab extra. In the former 
case the differences involve the character of parts as the 
concrete involves the abstract ; thus head, arms, legs in 
a man have quantitative relations to each other and to 
his whole figure, which vary only within narrow limits, 
and which sculpture or painting must not violate ; or 
again, his whole life is only possible subject to definite 
quantitative relations of energy supplied to work done. 
In the latter case the parts, indifferent in themselves, 
are forced by construction into the function of differences. 
The reservations to which this last assertion is subject 
have been explained above (see pp. 187-8). 

Thus equation and judgment are no doubt closely re- 
lated in their origin; and this is further illustrated by 
the facility with which judgment drops back or crosses 
into the equational form, which demands altogether less 
effort and insight than the attempt to grasp the differ- 
entiated structure of things. I cannot refrain from quot- 
ing in illustration a paragraph from a powerful and sen- 
sible writer whose one fault is the love of moving in the 
lower categories and avoiding the effort to grasp entire 
realities as they afe. ' As to the general result 1 [of 
human progress] what is it ? Say, roughly, three hundred 

James Fitzjames Stephen, Liberty, Equality, and Fraternity, p. 177. 

chap. iv. j The relapse into Number. 203 

million Chinese, two hundred million natives of India, two 
hundred million Europeans and North Americans, and 
a miscellaneous hundred million or so. Central Asians, 
Malays, Borneans, Javanese, South Sea Islanders, and all 
sorts and conditions of blacks ; and over and above all 
the rest, the library at the British Museum. This is the 
net result of an indefinitely long struggle between the 
forces of men and the weights of various kinds in the 
attempt to move which these forces display themselves. En- 
thusiasts for progress are to me strange enough. " Glory, 
glory : the time is coming when there will be six hundred 
million Chinese, five hundred million Hindoos, four hun- 
dred million Europeans, and Heaven only knows how 
many hundred million blacks of various shades, and when 
there will be two British Museums, each with a library." ' 
The numbers here are not merely descriptive ; they are 
essential ; otherwise the element of progress could not 
consist in their augmentation. Of all instances that show 
in what thin abstractions a writer who prides himself 
on contact with realities* may live and move. I know none 
more grotesquely striking than this ; and it cannot be 
defended by suggesting that its absurdities are in some 
degree imputed rather than adopted. For they can only 
be so imputed because they are adopted. The faith in 
progress need involve no assumption of numerical increase 
of population. Had the writer ever heard of virtue or 
knowledge? 1 That his main thesis in the passage is 
somewhat of a truism does not justify so gross a miscon- 
ception in supporting it. The more we examine the more 
we shall find that it is indolence which makes us drop 
into the equation when our subject-matter demands the 

I have finished the account of the equation before pro- 

1 Contrast Dante's lines : 

'Considerate la vostra semenza; 
Fattl non foste a viver come bruti 
Ma per seguir virtude e conoscenza.' 

Inferno, xxvi. 1 18. 

204 Abstract Quantity. [booki. 

ceeding with the judgment proper chiefly with a view to 
coherence in treatment, and not with an intention of repre- 
senting the former as inferior to or less ultimate than the 
latter, though in a sense which may appear from p. 91 above, 
such a representation might be held justifiable. But the 
conception of divergence, of a co-ordinate evolution gener- 
ated by abstraction, seems more appropriate to the matter 
before us than that of linear development 1 . The equation 
is, as we saw, hardly even a momentary phase in the 
growth of genuine judgment ; the two functions part com- 
pany almost as soon as their significance reveals itself. 

And quantity is more than one among many categories ; 
as the simplest point of view which admits of difference 
and system it aspires to be, and in one sense is, the sole 
category, or ultimate ideal of knowledge. It may be 
treated as sole category falsely or truly. It may be sole 
in the sense that though abstract, yet, subject to the 
reservations involved in its abstractness, it has universal 
applicability. Every science, as we read in Aristotle, 
assumes its subject-matter, and does not give an account of 
it. The schematic world of space, time, and mass is in this 
sense, as an object of science, beyond question ; it has only 
to serve as an abstract postulate in working with perceptible 
facts, and from this point of view is a truth, if not the truth 
about the universe as a whole. As enabling a coherent 
reflective view to be obtained of perceptible phenomena as 
a quasi-totality (always encumbered indeed by the infinite 
series), it is of immense scientific value and co-extensive 
with definite existence. For these reasons, again, the equa- 
tion the judgment of quantity is rather co-ordinate with 
judgment than a phase in its development. And still more 
is there reason for so considering it if we take account 
of the false employment of quantity as sole category. 
This false employment arises, or would arise, supposing the 
category of quantity to be considered not merely as co- 
extensive with determinate existence, but as, in its abstrac- 
1 Above, p. 91. 

chap, iv.] Truth and falsehood of Quantity. 205 

tion, the ultimate reality of all determinate existence, and 
consequently as furnishing the final ideal of science. It is 
obvious that the true use of this as of every category slides 
easily into the false one. Every science is occupied with its 
own abstractions. Every individual mind tends to magnify 
that with which it is occupied. The category of quantity, 
for reasons mentioned above, lends itself to universal appli- 
cation. It seems a short step from universal application to 
sole application, but it is the step from truth to falsehood. 
It is not made exclusively by votaries of physical science, 
nor perhaps by them chiefly. It meets us in theology and 
in philosophy under the form of the quantitative infinite as 
a sublime attribute of the Deity, or of soul life, or of the 
universe as contrasted with the ' finite ' mind of man. We 
find it again in barbaric or vulgar art, in as far as this relies 
for effect on mere magnitude, mere evidence of expended 
labour, or mere costliness of material. And we do also find 
it no doubt in a formulated shape wherever matter and 
motion are invested with the dignity of real existence in a 
sense and to a degree that degrades the individual and 
concrete realities of life into something secondary and 
fictitious. But it is plain that no such tendency is neces- 
sarily involved in the treatment of these abstractions as 
real characteristics of the perceptible world. There is no 
special virtue in non-atomic continuous extension, nor any 
especial iniquity in the resolution of material objects into 
systems of vortex-rings, if such resolution either is a 
good working hypothesis or represents a real fact. The 
only error is in taking either a hypothesis for a fact, 
or a fact for the sole fact in confusion, not in mere 

The category of Quantity is, as we have seen, in its \f 

nature wholly relative. It is therefore incapable of furnish- 
ing an absolute and ultimate account of things. It not 
only cannot escape from the reference ad infinitum from 
term to term and condition to condition, but is forced to 
make this contradictory conception the very basis and 

206 Abstract Quantity, [booki. 

postulate of its scheme. We have seen that the moment 
characteristic quantity or proportion makes its appearance 
in the judgment, as in any quantitative judgment it may, 
the whole between parts of which the characteristic propor- 
tions obtain is tending to exhibit itself as an individual 
synthesis of true differences, not as a mere aggregate of 
indifferent parts. The pure quantitative judgment or mere 
equation 1 is possible only by abstraction from one aspect 
of the essential judgment-function. It is not easy to find a 
parallel to so comprehensive and systematic an employment 
of a single class of abstractions, except in any attempt 
which may have been made to regard the world as simply 
a congeries of qualities, say of pleasures and pains. No 
such system indeed exists the point of view excludes 
system ; but one may conjecture of some such state of 
feeling as forming the consciousness of children and 
childish adults who have no judgment to pass on things, 
persons, or events beyond the expression of their likes and 

Thus I have thought it desirable to treat as in some 
degree co-ordinate developments the two series of judgments 
which diverge from the simplest measurement or equation 
such as a colour-match. On the one side we have the full 
evolution of concrete thought, as it builds up the actual 
and individual world within the series of relativity; on the 
other side we have the truncated evolution which embodies 
relativity almost pure and simple, but, as the abstraction is 
never quite complete (for then it would annihilate itself), 
may in particular matter revive its relation to totality, as 
we see in the exhaustive judgment of enumeration, and in 
the quasi-generic judgments of geometrical classification. 
And in the same way the more concrete judgment may 
in particular phases and under particular stimuli borrow 

1 An equation that embodies a characteristic proportion is not purely quan- 
titative. It involves in its interpretation the material differences between the 
parts which are in the assigned ratios, e. g. between angle and arc. See p. 186, 

chap, iv.] Meeting-points of the two series. 207 

determinations from or generate approximations to the 
abstract series. This happens when the life of a nation is 
subjected to statistical treatment; when the disjunctive 
judgment is taken in the weakened form of enumerated 
alternatives, and so gives rise to the calculus of proba- ^ 
bilities ; or when any one of the grooves or threads of 
relativity which compose the perceptible world is taken as 
a problem per se and tracked to its consequences by means 
of a pure hypothetical judgment. 


Singular and Universal Judgment. 

Singular i. The transition from the singular to the universal judg- 

Judgment. ment j s ^ transition from the affirmation of particular fact 
to that of general fact. This transition may be expressed 
by distinguishing two forms of the singular judgment, which 
may be called respectively the Individual and the Corporate 
Individual i. In approaching the Individual Judgment we are return- 
judgment. j n g f rom ^g one-sided offshoots of measurement to the 
normal and concrete evolution of the judgment. We saw 
in chap, iii that it is the judgment of proportion which first 
reveals individual quality ; that is, quality which, although 
particular and characteristic, yet does not refuse to admit 
diversity into itself and itself to enter into various contexts. 
This quality, however, we found, if merely indicated as the 
content of an abstract idea, stood in antagonism to the 
demonstrative indication of present perception which alone 
could attach it to actual reality. We found ourselves en- 
tangled in such judgments as ' This oak-tree has a leaf-spiral 
of f,' 'This teasel has the bracts longer than the head,' 
1 This tower diminishes in width from story to story.' Such 
judgments as these must rank as singular, for it is of their 
essence to qualify present perception by the meaning of 
ideas ; yet their content is really ambiguous, for, as we saw, 
the designative idea which ekes out the demonstrative refer- 
ence to the concrete subject tends to grow into a condition 
and to make the judgment abstract, and in that sense 
judgment a. The ambiguity which tends to split in two the im- 
withProper p er f ect singular judgment of the above type, which we have 

Proper Name indicates Universal. 209 

ranked among the judgments of measurement, is apparently- 
removed in the class of singular judgments which we now 
proceed to consider, and which are avowedly based on the 
fact of recognisable individuality. Such are judgments 
whose subjects are designated by Proper Names. Enough 
has been said in the Introduction of the essential nature of 
Proper Names. We have now only to consider the logical 
value of the judgments which are made by their means. 

The determinate idea, present in the judgment of pro- 
portion, is omitted in the judgment made by means of a 
proper name. On the other hand, the demonstrative 
particle, which by itself is helpless, being only an indefinite 
reference to presentation, is replaced in the proper name by 
the indication, not to be effected without some kind of 
meaning, of a particular individual. Thus it might be said 
that the two elements of the subject in such a judgment as 
'That young soldier is the victor of Actium' are fused 
together in the subject of ' Caius Julius Caesar Octavianus 
is the victor of Actium.' But the union is effected at the 
cost of a mutilation of the significance ; although as in the 
present example the diminution of determinate content may 
be more than compensated by the accession of suggested 
ideas. Identification no doubt involves ideas, but with the 
proper name, as we saw, identification is the end and ideas 
are only the means. In unfamiliar matter, say in a chronicle 
of remote date, we might conceivably identify the unknown 
possessor of some name as figuring in several scenes or 
incidents without being sure what he, she or it might be ; 
whether a man or a woman, or a favourite horse. In this 
sense the judgment that deals with a proper name is merely 
particular. It has no meaning that can carry its application 
beyond the unique individual to whom it is taken to refer. 

But, though subject to this imperfection, yet Singular 
Judgments of the class now before us form a real advance 
on the Singular Judgment of Proportion. They rest upon 
the fact of characteristic individuality capable of change and 
persistence without sacrifice of identity. Instead of an 

VOL. I. P 

2io Singular and Universal Judgment, [booki. 


with Name 
and Ideas. 

abstraction limited by pointing as if with the finger they 
refer us to a unique concrete thing in its continuous perma- 
nence. In this sense, because attached to a continuous 
element of reality not shut up within a particular time or a 
given perception, the Individual judgment is universal, and 
as we shall see leads up to a transition which takes us in 
one respect beyond the Singular Judgment. But universality 
concrete universality is not, we must understand, anta- 
gonistic to individuality. ' Caesar crossed the Rubicon' is an 
individual Judgment ; yet in it we are not 1 confining the 
reference of Caesar to the moment in which he was engaged 
in fording the river. If we thus refused to refer the predi- 
cated content to the whole extended identity of Caesar the 
significance of the judgment would be destroyed, and an 
eristic error committed by reducing an assertion to a 
tautology. Where is the significance of crossing the 
Rubicon if we do not affirm it of the conqueror of Gaul, the 
rival of Pompey, and the true founder of the Roman 
monarchy? Thus the judgment regarding a person, place 
or other object that bears a proper name introduces a refer- 
ence that is determinate without being abstract, and par- 
ticular without being confined to present perception. It 
should be observed that not all classes of objects are suited 
to be distinguished by proper names. This fact is akin to 
the inapplicability of significant names indicating a thing to 
many objects endowed with material existence. The range 
of proper names falls within that of significant names of 
things, and the spheres of application of these two kinds of 
symbols compared with each other and with the sphere in 
which neither applies have a curious bearing on the subject 
of individuality (see above, p. 138). 

/3. With these Individual judgments must be classed all 
predications dealing with particular events, individuals, or 
objects, in which the demonstrative particle is dispensed 
with and replaced by a symbol referring to the individual. 
It will be found that these particular events, persons or 

1 Contrast Lotze, Logik, sect. 58. 

chap, v.] Personal and objective era. 211 

objects have ultimately to be designated by reference to 
a proper name, or to some symbol which nearly approaches 
the nature of a proper name. As such e.g. may be ranked 
all chronological indications 'Christmas Day, 1885 A.D.' 

It is obvious that such a symbol, or a proper name, as a 
fixed point in history, may be supplemented by any amount 
of definitely significant ideas ; and as the proper name or the 
date is often understood or presupposed, e.g. in a continuous 
narrative, we are apt greatly to under-estimate the part 
played in judgment by the content of such symbols. Page 
after page of discussion about political or social tendencies 
may chance to be found fn a reflective history, say in 
Lanfrey's History of Napoleon, without the mention of a 
proper name. But in so far as these discussions are to be 
taken as significant of the actual conditions of an actual 
epoch, they are understood as ideal content predicated of 
the nation, age and persons with whom the narrative is 
concerned. Chronological symbols exhibit the transition 
from the demonstrative to the proper name in a peculiarly 
clear light. ' To-day,' ' yesterday,' ' last year,' are just on 
the line between demonstratives and proper names. ' To- 
day' seems naturally to = ' This day,' a demonstrative indi- 
cating mere relation to the percipient subject 1 . 'Last 
year/ ' twenty years ago,' show the relation to the percipient 
subject growing into an objective system. And when we 
come to the employment of an era, A.U.C., B.C., A.D., we 
have the system transferred from the accidental percipient 
subject, and attached to the content of a proper name. 
Wherever we have ' I ' or ' my' etc. as points of reference in 
narration, we are dealing with something between a demon- 
strative and a proper name. And every narrative judgment 
which goes beyond a mere impersonal or demonstrative 
reference to present reality or to my own perception may 

1 I take what I believe to be the actual meaning in use. Philology may or 
may not support it as the original meaning. We are bound to take philology 
into account as evidence of evolution and as a guide to observation ; but it 
cannot override present usage. 

P % 

212 Singular and Universal Judgment, tbooki. 

prima facie be said to involve a reference to some proper 
name. No mere abstract idea can form the subject of 
historical predication. How far this prima facie conception 
must be corrected by allowing for judgments which may be 
capable of uniting without mutilation the powers of unique 
reference and of determinate notions is a question which 
will occupy us in the sequel. 
Corporate ii. Closely allied to the Individual Judgment, and perhaps 
ju gmen . n r jgj^ technicality not distinguishable from it, is what for 
want of a better name I call the corporate judgment. This 
title is meant to include all such affirmations as deal with 
comprehensive totalities or aggregates which we bona fide 
take in their corporate or singular aspect, and do not con- 
sider either as in the collective judgment, in the light of 
sums of enumerated particulars, or as in the hypothetical 
judgment, in the light of mere abstractions whose very 
existence is not absolutely postulated. Such a judgment 
may be expressed indifferently by a singular or by a rfliiral 
enunciation, so long as the name used in the plural is a bona 
fide designation of a known or knowable unity in respect of 
its characteristic features: e. g. ' The ancient Greeks were at 
once a most scientifically and a most imaginatively minded 
race.' This judgment obviously = ' The Greek race was,' etc. 
This is not a collective judgment in the sense which has 
above been given to that title. It is not capable of being 
obtained by successive synthesis of the component units 
by enumeration and retains therefore no special exten- 
sional reference to the individuals who as an aggregate 
constituted the ancient Greek race ; it starts from the idea 
of a common stock as a historical entity with peculiar 
endowments and with its own rise, decline and fall. Other 
instances are such as ' Europe has acted harshly to the 
modern Greek nation.' Europe is here not a geographical 
expression, nor even a mere body of nameable states ; it is 
an organisation acting upon definite resolutions and through 
a known combination and proportion of forces. Several 
states in geographical Europe probably do not count in 

chap, v.] Historical realities, 213 

political or concerted Europe. Again, we may say * The 
House of Commons detests a bore.' This might be trans- 
formed into ' All members of the House of Commons ' etc., 
but the two affirmations are only equivalent if the latter is 
understood of the members qua members, i. e. as engaged 
in debate in the House; otherwise this latter becomes a 
mere collective judgment, dealing with the members as a 
collection of individuals who share two attributes, viz. 
belonging to the House of Commons and hating bores, 
but wholly neglecting any reference to the House in itself 
as a single body with its own functions and peculiarities, 
among which is the one predicated in the judgment. The 
glacial period, The French Revolution, The Italian renais- 
sance, The solar system, are ' corporate ' realities and sub- 
jects of singular judgments of the species of which I am 
now speaking. 

The distinction between such individualities and those of 
really single objects or persons such as form the subjects of 
individual judgments is not a matter of principle, for in both 
the existence of the subject is affirmed, or, as I prefer to 
say, absolutely postulated. Nevertheless, the fact that 
such individualities as we have now before us do on one 
side consist of immense aggregates of particulars, and are 
therefore capable of being regarded at any moment from 
points of view antagonistic to that of their individuality, 
either as abstract ideas or again as series of numerable 
units, makes it desirable to mark by a specific distinction 
the fact that in their unity they can be regarded as indi- 

On the other hand, the subjects in question are again not 
easy to distinguish absolutely from the content of scientific 
class conceptions whose individual unity and actuality are 
disputable. The line which I have drawn is intended to 
correspond with the distinction between history on the one 
hand and truly physical science on the other. History 
deals on the whole with contents into the essence of which 
time enters, and which therefore, however comprehensive, 

214 Singular and Universal Judgment, [booki. 

are ultimately particular within the phenomenal series. 
Abstract science as a rule deals with timeless connections 
and systems of attributes, though it will be necessary in 
exhibiting this tendency to make allowances for a consider- 
able admixture of and recurrence to the historical attitude, 
for in the light of evolution, time, or at least amount of 
change, enters into the essence of most things. And 
besides Abstract Science we must not leave out of account 
Classificatory Science on the one hand and Philosophy on 
the other, both of which, though in different senses, may 
claim to deal with actual realities. 

The Corporate Judgment marks the fullest development 
of the affirmation of particular fact, and at the same time a 
near approach to the affirmation of general fact. In other 
words, the affirmation with which we have so far been 
dealing, is beyond possibility of dispute Categorical affirma- 
tion, treating of contents which the judgments affirm, or at 
least absolutely postulate to be features that have or have 
had actuality in the world continuous with present percep- 
tion. But from this point onwards the Categorical character 
of judgments becomes a matter of theory and of analysis. 
There is indeed, according to the scheme here adopted, no 
absolute separation between the Singular and the Universal 
Judgment. Still the distinction, unknown to Formal Logic, 
which is the ground of that separation as made by recent 
writers, is the basis of our scheme also. The Historical or 
Singular Judgment, and a fortiori the perceptive or im- 
perfect singular judgments that precede it in our scheme, 
are not on all fours with the judgments of science, whether 
classificatory or analytical, or of philosophy. Before 
attempting to trace in these latter types of judgment the 
elements which we have observed in the former, though in 
other proportions and combinations, it will be well to 
examine more particularly the one leading difference 
between the two chief stages of affirmation. 
Time and j^ y/he Judgment that asserts particular fact coincides 

existence in * . - _ . , 

Singular with the Categorical Judgment in the primary sense of 


chap, v.] The time in Predication. 215 

the latter title. According to the standpoint which for 
the present we have adopted, a judgment is Categorical 
when it asserts some thing or event to belong to the actual 
world in which we live. This assertion is made both by the 
Individual and by the Corporate Judgment. For the 
subject in these judgments is something that can exist as a 
particular reality, and is therefore taken or presupposed to 
be a real particular, while at the same time its reality is so 
far determinate that it can intelligibly be denied, which we 
saw not to be the case with the ' this,' ' here,' or ' now ' of 
the Imperfect Singular Judgment. In these judgments, 
therefore, though not necessarily in them alone, we have 
existential assertion. And the simplest test of the presence 
of such an assertion is to ask whether the non-existence in 
reality of the content which enters into the judgment 
renders that judgment false. To such a question the 
primary answer is that at least in all judgments where 
time enters into the content i. e. which assert facts 
in time the non-existence of this content renders the 
judgment false. And these judgments will be found to be 
coextensive with the Historical Judgment, affirming as it 
does not necessary connection, but particular reality within 
the phenomenal series. And thus, as said above, the His- 
torical or Singular Judgment is equivalent to the Cate- 
gorical Judgment in the sense here under consideration. 

This answer, however, demands explanation and limita- 
tion. If non-existence of the content or subject of a judg- 
ment renders the judgment false, we have further to ask, 
Non-existence when ? " 

In every judgment we must distinguish between the time 
of predication and the time in predication. The time of J 
predication, i. e. the time at which some thinking being 
makes the judgment, is relatively to the content of the 
judgment a mere accident, and alters actually while we are 
occupied in judging, and a fortiori when the judgment is 
rethought after a lapse of days or years. The time in pre- 
dication is the relation of the predicated content to the 

216 Singular and Universal Judgment, [booki. 

total content of the temporal series of events which we con- 
struct and contemplate as objective. The time in predica- 
tion, if any, is affirmed as an attribute by the judgment ; 
the time of predication is not affirmed as an attribute by 
the judgment, which therefore is not made false by any 
relations whether negative or positive between its content 
and that time. Hence it follows that the non-existence of 
the individual subject or content which falsifies a Singular 
Judgment is non-existence at the time in the predication, not 
non-existence at the time of the predication. 'Thucydides 
is among the greatest historians of the world ' is not false, 
although Thucydides is in fact, when we speak, not a living 
man 1 . ' The House of Commons is an integral part of the 
British Constitution ' does not depend for its truth on 
Parliament not being in dissolution at the moment of pre- 
dication, but only on the co-existence of a House of 
Commons with the British Constitution in the sense and to 
the extent demanded by the import of the judgment. It 
appears to be a corollary from this principle that if no time 
in particular is involved in the import of the judgment, 
which is the case at any rate with geometrical truth, it 
becomes all but impossible to convict a judgment of falsity 
on the score of non-existence of its content ; although 
the demonstration of utter non-existence, i. e. I suppose of 
impossibility, would so convict it. This bears on the 
categorical character of the generic and hypothetical judg- 

A subtlety is introduced into the problem by the 
phenomena of tense which include the time of predication, 
or a relation to that time or personal era, within the con- 
tent of the judgment, and so within the allegation of time in 
the predication. The content so superadded is of the most 

1 It may be objected that it is false to say ' Thucydides is a general in the 
Peloponnesian war,' simply because Thucydides does not exist at the time 
of predication. Where we have true tense this is so; we have then not 
got rid of the personal era. See p. 3 IX. It must be remembered that in 
Thucydides was ' etc. Thucydides is non-existent, and yet the judgment 
is true. 

chap, v.] Tense and Personal era. 217 

fugitive and relative nature, and is constantly neglected 
even by historical narrative. Picturesque history neglects 
it by the use of the historical present, and philosophical 
history by the use of the logical present. Nevertheless 
where a past, future, or true present tense (neither historical 
nor logical) is intentionally employed, its relation to the 
personal era or date at which the narrative is drawn up 
beyond a doubt enters into the judgment and makes an 
assertion which demands a particular limited existence on 
the part of certain objects and events, and is false if this 
existence is not as affirmed. In the case of the present 
tense there is a peculiar subtlety arising from the confusion 
between the atomic or nearly atomic and the continuous or 
ultimately non-temporal present. The former is the im- 
port of the present as a true tense ; the latter of the present 
as it approaches to a mere vehicle of affirmation. Compare 
the following examples : ' The Derby is being run at this 
very moment;' ' The horses are leaving the paddock for the 
Derby of 1861 ' (from a narrative written in 1883) ; 'The 
Derby is run once a year ; ' ' The Derby race in England 
is an instance of those customs which owe nothing to 
government but yet amount to national institutions.' The 
first of these judgments if true now must be false after the 
lapse of five minutes. The second is only false if there was 
no paddock or no Derby in 1 861. The third is only false if at 
the time of its predication the race has altogether ceased to 
be an annual event ; but its present is well able to compre- 
hend within itself the intervals of time which the import of 
the judgments admits and requires, and is not falsified by 
reason of the non-existence of the race during these annual 
intervals. And the fourth is false only if there never was 
nor will be such a thing as a Derby race having the im- 
portance alleged in English life. I am discussing of course 
only how far the respective judgments become false if we 
assume non-existence of the content ; I am not raising the 
question of the material truth of the attributes enunciated. 
It is only in the first of these four examples that we see the 

218 Singular and Universal Judgment, [booki. 

present operative as a true tense. In the case of the past 
and future the difficulty of tense does not arise in its full 
extent ; the tenses which indicate them must of course 
introduce the personal era, but for that very reason cannot 
be confused with a mere form of predication, for which they 
have not the appropriateness that the present possesses. 
Therefore they do not risk the reduction of every possible 
judgment to a statement about a momentary date or 
epoch, which would be the result of neglecting the above 
distinctions in the use of the present tense. And moreover, 
these very tenses f was ' and ' will be ' prove that it is at 
least not necessary to the truth of a judgment that its con- 
tent should exist in the moment 0/ predication. It is how- 
ever necessary for judgments dealing with past and future 
that their content should have the alleged relation, however 
fugitive and accidental, to the time of predication. But at 
any rate in none of these cases, neither in present, past nor 
future, need the content be shut up within the time of pre- 
dication or the time related to that personal era. Past and 
future do not pretend to be momentary, and the present 
cannot possibly succeed in being so. It must be credited 
either with duration in itself or with a continuity that shades 
by degrees into the past and future. 

Thus, though the time of predication has the slightest 
possible relation to the content of judgments, yet no doubt, 
when predicated as an attribute by help of true tense, a re- 
lation to the time of predication or subjective era enters 
into predication. And in so far as history as a whole falls 
in the past, the use of the past tense in narrative bears true 
witness to the essential particularity and limitation of the 
existences with which history deals. But after all, the past 
is not a point but a line ; and so for precise temporal im- 
port even of narrative propositions in the past tense we 
must go, not to the tense, but to the import of the judg- 
ment. And a fortiori this is the case with the present, 
where the true tense is difficult to distinguish from the 
same tense used as the mere form of predication. 

chap, v.] Defects of Singular Judgments. 219 

We have thus seen in what sense and to what extent 
Singular and Perceptive Judgments are identifiable with 
Categorical affirmation. The Judgment whose content in- 
volves a limitation of time is plainly false if in the time- 
relation prescribed by such a limitation its content is non- i 
existent. This test shows that all such Judgments are 
assertions of particular fact. Even the example (on p. 217) 
which goes beyond common historical usage nevertheless 
asserts fact which is essentially in time, although the truth 
of the assertion is not relative to the date of predication. 
If the Derby race never existed the judgment would be 
false, and its existence involves a multitude of temporal 
relations which are necessary to its being what it is. It is 
essentially a fact in time. 

When we get away from the proper name and the re- 
lations of events in the temporal series, we find it much 
less easy to say what non-existence of particulars, if any, 
would imply the falsity of the judgment, and in what sense 
therefore, if in any, the judgment alleges actual fact be- 
longing to the real world. We must bear in mind that we 
have up to this point been dealing with unanalysed per- 
ceptions and with proper names and their expansions. We 
have therefore not got rid of the element of irrational con- 
creteness which attends all judgment whose subject is 
given as if by simple pointing with the finger ; for qua a 
mere symbol of identification the proper name itself par- 
takes of the character of simple pointing ; and until we 
reached the proper name we were encumbered with the 
demonstrative particle. 

Therefore the judgments thus far considered, omitting 
the one-sided forms that arise out of measurement, possess 
certain peculiarities. They assert, to begin with, the 
existence of things or events in time. In doing so, they 
restrict and burden with irrelevant matter the application 
of determinate ideas, which, as the only symbols of mean- 
ings, they cannot avoid employing. Taken therefore as 
rational connections of attributes, a point of view which 

220 Singular and Universal Judgment, [booki. 

determinate ideas challenge, and towards which, as we saw, 
the import even of proper names tends to develope, the 
judgments which we have been considering axe false, being 
burdened with irrelevant and deficient in relevant matter. 
This is the same thing as to say that they present an as- 
pect of necessity, in which aspect they are defective and 
so false. 
The 2. By the title of ' Universal Judgments ' I mean to desig- 

Judgment. nate ' m a ^ their phases of import, the assertions usually 
typified by such well-worn examples as 'All men are 
mortal,' I All fire burns,' and ' All triangles have their three 
angles equal to two right angles.' It has been shown 
above that perceptive and singular judgments, and more 
especially those which employ proper names, possess an 
element of universality as predicating identities into which 
differences enter or which persist through differences. But 
in spite of this fundamental unity of the judging function, 
the distinction between the 'Singular' and the 'Universal' 
Judgment has an importance for us which it has not for 
traditional Logic ; which indeed treats the Singular and 
the Universal Judgment as on the same level in a strictly 
logical point of view, and both, consequently, together 
with the particular judgment, as species of Categorical 
enunciation. The attitude which we have to adopt to- 
wards this arrangement was defined in an early part of 
the present book *, where we saw that it was impossible 
for us to retain these species of enunciation in their tra- 
ditional relations. It is beyond a doubt that the Uni- 
versal assertion must at some point of its development 
assume in some aspect or in some degree a hypothetical 
character ; while if the genus Categorical, which certainly 
includes the singular judgment, extends into or over the 
domain of the Universal, it can only do so subject to re- 
servations which are unnecessary so long as it is confined 
to the judgments of present perception or of simple nar- 

1 See suj>ra } chap. i. p. 93 ff. 

chap, v.j Universal distinguished from Singular. 221 

The Universal judgment, then, is not distinguished from 
the Singular judgment by the mere feature of Universality, 
but by a special phase of Universality, that is to say, by 
the predication, of a universal law of connection. It has, 
indeed, been obvious to us throughout the analysis of 
judgment that universal connection was everywhere at 
work in the background, exploiting any qualification ex- 
pressed or implied in the Subject, for the benefit of sys- 
tematic connection or necessity, and at the expense of the 
simple perceptive or narrative conjunction of contents; 
until, surrendering for the moment the task of intelligible 
qualification of reality, we fell back, in the proper name, 
on an attempt at unique designation \ But here again we 
fail to escape from universal connection or necessity, and 
in the names of illustrious individuals, as in those of na- 
tions, epochs, or movements, we have found that every 
significance tends to break down the mere conjunction of 
data, and to exhibit itself as a connection of reason and 
consequent. We attempted to draw the line at events and 
individuals into whose content time entered, and to show 
that judgments dealing with such matters as these were 
inevitably allegations of fact, and not of abstract connec- 
tion. Now we adhere to this distinction, and it is per- 
fectly true that any fact which is especially involved in 
one portion, however extended, of the temporal series of 
phenomena, must have existence within that portion if 
an affirmative judgment about it is to be true. The as- 
sertion of such a fact in its accidental concreteness is 
therefore radically different from the assertion of a mere 
law or relation, and if taken in this latter sense would 
necessarily be false. But we found in the corporate judg- 
ment that it was not perfectly easy to distinguish the facts 
of history from the truths of science; for sets of events 

1 I have said above (Introduction) that I do not give this as a historical 
account of the genesis of proper names, which must no doubt have been applied 
and recognised by a gradual differentiation. But none the less, wherever 
language has fixed them as a class of words, they perform the function and are 
subject to the modifications indicated in the text. 


222 Singular and Universal Judgment, [bookl 

greatly extended in time appear to pass by a sort of 
sorites into sets of events which, though in respect of ex- 
istence precisely on all fours with actualities limited in 
time, are nevertheless either not treated as relative to time 
or really are not held to be so relative. In order, while 
marking the distinction demanded by the absence of 
limited particularity, to give full weight to the continuity 
of import between these types of judgment, I shall not 
follow Lotze and other modern writers in identifying the 
universal ab initio with the hypothetical judgment. I 
shall prefer to distinguish within it two species, of which 
the first, the generic judgment, alone belongs to the main 
evolution of thought, and the second, the pure hypothe- 
tical, is regarded as an abstraction of a quasi-mechanical 
character, and consequently as a divergence in the direc- 
tion of the arithmetical and geometrical judgment. 
The i. The generic judgment is the qualification of reality 

Judgment, under the aspect of a Natural Kind by attributes or re- 
lations incident to that Kind. A Natural Kind is for our 
purpose a Kind accepted and treated as such by any science. 
We have already seen that the geometrical sciences are in 
this respect in a peculiar position, and we have discussed 
the limits under which their quasi-generic judgments may 
be taken to embody truth about actual reality. The 
question of alternative classification, which arises on account 
of the different points of view introduced by different 
sciences, was treated in the Introduction, and should cause 
us no difficulty if we are once able to understand the nature 
of the truth embodied in any science. For every science 
employs some abstraction and idealisation, though there is 
an all-important difference of degree between contents 
which are merely abstract as not sensuous, and contents 
which are abstract as not concrete. 

The restriction { incident to that kind ' is not intended to 
exclude relations which one kind shares with other cognate 
kinds. A purist logic, following a suggestion to be found 
in Aristotle, might indeed require that every generic judg- 

chap, v.] Graduated Identity. 223 

ment should be ' commensurate' or characteristic. It would 
then have to deny that the possession of breathing apparatus 
was incident to man, because he shares the respiratory- 
function with the whole organic world. Such a view would be 
illustrated by the fact which was commented on above, that 
e. g. the animal properties of man are, in man, modified by 
their relation to his humanity; so that in order to represent 
them as features of man they ought ideally to have certain 
modifications assigned to them, while in their abstraction 
they can only be set down as characters correlative to the 
no less abstract idea of animality as such. But this prin- 
ciple seems needlessly purist. The attributes which man 
shares with the animal world are elements of identity, 
however partial, between him and it ; and there can be 
no reason against characterising him by these identities 
which would not tell equally against any knowledge which 
falls short of perfection. The rule to be borne in mind about 
such cases is that imperfect knowledge only becomes false 
when mistaken for perfect knowledge. In as far therefore 
as the form of the judgment implies a truth completely 
adequate to its subject, something may be said for the view 
which has just been stated. But we shall find if we press 
the matter home that this ideal is to be regarded as the 
vital principle active in knowledge, but not as hostile to any 
genuine fact that is free from confusion. 

Under 'incident to the kind' then are included the 
attributes and relations which lie at the root of the indi- 
viduals' being, although shared by them with individuals 
of other kinds, or even with mechanical cur geometrical 
wholes. It is only to be borne in mind that such relations, 
e.g. the characters of vertebrate organisms, are not thought 
as mere abstract properties, when applied to specific kinds, 
but are regarded as concrete schemes presenting both a 
general and a specific aspect. It is in this characteristic 
of graduated identity that the intelligible order of the 
world reveals itself to us. 

The generic judgment has always been the battle-field 

224 Singular and Universal Judgment, [booki. 

of conflicting logical tendencies, corresponding to actual 
needs and features exhibited in various points of view by 
the judging activity. I shall endeavour, on the same plan 
which I have hitherto pursued, in some measure to satisfy 
these tendencies by distinguishing as different, in phase and 
line of evolution, intellectual acts which are often reckoned 
as one and the same. But it follows from the nature of 
thought that all such aspects have a real connection, and 
are in fact rather distinguishable than separable. Thus in 
distinguishing the generic judgment from other acts of 
thought we shall also be analysing this many-sided judg- 
ment itself and justifying to some extent the views of 
those who have recognised in it only one or other of its 
many sides. 
The a- The Generic Judgment the Universal Judgment of 

^f sl ". common life and of classificatory science was regarded 

collective f & 

Judgment, by Aristotle, as is well known, under two connected 
aspects, as a judgment of Allness and as a judgment of 
Necessity. The former of these aspects has been seized 
on by formal logic, and the doctrine of logical universality 
has been adapted mainly to the consideration of subject 
and predicate as names or ideas applicable to groups of 
individuals. We examined the judgment from this point 
of view, as dealing with an aggregate arising out of enume- 
ration, in a former chapter. We there saw its actual goal 
in the Collective Judgment and its reversion towards a more 
concrete and natural mode of thought in the Exhaustive 
Judgment, which amounts to nothing but a Generic Judg- 
ment very .strictly taken in extension. It must however 
be remembered that we did not think it possible for 
any judgment, however closely confined to an aggregate 
resulting from enumeration, to avoid designating the in- 
dividuals by a common attribute, and predicating an 
attribute of them. Attributes are enunciated by exten- 
sional no less than by intensional judgments ; but in the 
latter .they are connected with attributes, in the former 
they aire centred in the identity of individuals. Therefore 

chap, v.] Quasi-collective Generic Judgment. 225 

it is possible to consider the Generic Judgment as differing 
from the Collective Judgment simply in degree, viz. by- 
predicating attributes of an unknown or unlimited and not 
of a known or determinate aggregate, the actual means 
of predication being in both cases alike a general attribute, 
though in the latter case attached to reality by a proper 
name or its equivalent. But an unknown or unlimited 
aggregate of individuals is a contradiction 1 , a numerical 
problem which proclaims itself insoluble by enumeration, 
and therefore the judgment which is couched in this shape, 
and which in fact conveys a perfectly intelligible meaning, 
must derive this meaning from some other source than 
from such an enumeration as that on which the collective 
judgment rests. The Exhaustive judgment must be inter- 
preted by the Generic and not by the Collective. 

Examples of the Quasi-collective judgment of which we 
are speaking are 'All men are mortal,' 'All organisms both 
breathe and assimilate,' 'All unstriped muscle in the human 
body is inaccessible to the control of the will.' This last 
example, however, is suggestive. The Exhaustive judgment, 
i.e. the Generic judgment in its aspect of ' allness,' is helpless 
in the face of the most trivial exception. Thus ' Nearly all 
striped muscle is under the control of the will,' but the muscles 
of the heart form an exceptional case, and, though striped, 
are normally inaccessible to volition. Nevertheless there 
can hardly be a doubt that the coincidence expressed 
by the judgment must indicate some sort of connection, 
however circuitous, between the appearance of the muscle 
and the degree in which it is under control, and that 
the exceptional case must be accounted for by special 
conditions. But on its purely enumerative side the judg- 
ment has nothing to say to this ; it only knows that 
the sum-total of Enumerative judgments cannot be made, 
and the judgment of allness is therefore unwarranted. It 
is obvious that the affirmation of universal connection 
which in such an instance we feel to be all but warranted 

1 See p. 175, supra. 
VOL. I. Q 


226 Singular and Universal Judgment, [booki. 

is not approached from the side of the individual units, 
but from the side of the common or continuous nature 
which binds them into a whole. 
True Gene- }. As dealing with a common or continuous nature the 
merit. Generic judgment may be more properly expressed in the 
form, ' Man is mortal,' ' Water boils, under one atmosphere, 
at 212 Fahrenheit,' 'A society organised on a purely com- 
mercial basis treats the working classes as little better than 
slaves.' These propositions are accepted as practically 
equivalent to 'All men are' &c, 'All water' &c, 'All 
societies' &c. Here however it is plainly the connection 
of attributes that warrants the affirmation concerning indi- 
viduals and not vice versa. When thus regarded, the 
Generic judgment challenges comparison with the Singular 
judgment in both its forms, both as Individual and as 
Ordinary a. ' Man is an animal capable of social life,' ' The bacillus 
Analogical ls a septic organism,' ' Throughout the vast Orchidean 
Judgment, order, including 433 genera and probably about 6000 
species, the act of fertilisation is almost invariably left to 
insects.' These are affirmations that unquestionably refer 
to something real, but yet employ neither perception nor a 
demonstrative nor a proper name. Therefore, prima facie, 
it seems as if the determinate idea had come to its rights, 
and were no longer obscured by any irrelevant elements of 
the phenomenal concrete. The act of thought ought, it would 
appear, to fall at once into the groove of abstract necessity : 
t If man, then social;' 'If Orchid, then insect-fertilised.' 
But ideas such as those now before us offer a resistance to 
such treatment. The determinate idea is abstract, indeed, 
as all thought is abstract, but nevertheless it may have a 
content which is concrete, and in the example before us we 
have such concrete contents. These, therefore, bear the 
morphological character of individuality, by which alone 
even the unique object named by a proper name is made 
recognisable, persistent, and so universal. Compared with 
such an individual subject the Generic subject has lost unique 

chap, v.] Abstract, in Form and Content. 227 

reference ; but it has gained abstract significance, with which 
the proper name was incompatible. And it is in virtue of 
this significance, the significance of individual self-complete- 
ness, that the Generic subject persists as an identity through 
the differences which form its attributes. Now the indi- 
viduality when reduced to a content is not single, but exists 
in instances. Thus, in attaching differences to the individually 
characteristic content as such the judgment goes altogether 
beyond the synthesis of differences in an actual individual 
subject, and affirms such a synthesis mediately of a number 
of subjects, which may be taken as endless seeing that its 
limit is at this stage not held essential and not enquired 
after. Such a judgment, which treats a concrete individu- 
ality as an abstract universal, and extends its incidents to 
all individual instances, may be described as an analogical 
judgment. And this is the fundamental nature of the 
ordinary Generic assertion. 

The introduction of the term analogy into the theory of 
judgment may indeed be objected to on the ground that 
analogy is a kind of inference. But the fact is, that apart 
from any general question of a connection between judgment 
and inference, we are now at any rate on the threshold of 
an activity of judgment in which inference is unmistakably 
present. All that we can do in order to avoid a premature 
discussion of inference is to approach the analogical judg- 
ment rather as a conclusion the content of which is open to 
analysis than as a complete inference whose process lies 
before us. It may be added, that logic is quite familiar 
with the idea of 'necessary' judgments. Yet necessity 
involves inference far more explicitly than does analogy. 

In the analogical or ordinary generic judgment, then, we 
have neither implied reference to perception as in the im- 
personal judgment-form, nor the demonstrative 'this' or 
4 that,' ' here ' or ' there,' nor a conventional implication of 
unique reality by means of a proper name. The subject 
I speak of the immediate subject or subject within the judg- 
ment is an idea, and qua idea, is abstract. But we must 


228 Singular and Universal Judgment, [booki. 

distinguish between abstractness as incident to thought in 
contrast with sense-perception, and abstractness as a cha- 
racter attaching to contents present in thought. In the 
former way of speaking all thought is abstract. In the 
latter, some is abstract and some is not. The ideas which 
form the subject of the generic judgment in the phase now 
before us are not abstract in the latter sense. They are 
ideas of totalities, existences complete in themselves, to 
which we cannot indeed venture to apply the conceptions 
of teleology proper except in so far as the wholes in ques- 
tion are products due to the human mind, but which must 
be regarded from the standpoint of that secondary finality 
which may be described as morphological unity or quasi- 
teleology. We have thus a character or complex of 
attributes which is at once general and individual, abstract 
in thought and concrete in content. As abstract, it defies 
enumeration of instances, and implies necessary sequence 
or connection of attributes. As individual and concrete, on 
the other hand, it refuses to be taken as a mere ideal ante- 
cedent in a relation of necessity, i. e. of reason and consequent. 
The conciliation demanded by these antagonistic elements 
of import is found in the judgment of analogy. The essence 
of this judgment is that it is neither purely subsumptive, as 
expressing a de facto conjunction of attributes in a single 
subject, nor purely constructive as expressing a de jure 
connection of attributes independent of the immediate subject 
in which they may exist, but is something intermediate, as 
expressing a perception or presumption that the content 
enunciated in the judgment is bound up with the character- 
istic individuality which forms the immediate subject. 

The ultimate foundation of any such insight must be the 
final cause or teleological idea of the individual, which how- 
ever, when considered as an immanent or embodied final 
cause, is most prudently treated on the level of morpho- 
logical character. We may indeed safely say that the 
purpose or final cause for which we make a microscopic 
lens is to combine magnifying power with light and defini- 

chap, v.] Morphological Unity. 229 

tion, and from this purpose, by help of a number of further 
judgments dealing with optical and mechanical truths, the 
physical attributes of a good lens may be constructed. But 
in dealing with things not made for a known purpose we 
cannot apply any such abstract rule, and must fall back on 
the idea that the thing discharges an actual function, or at 
least looks as if it had a function, which must be taken as 
immanent and identified with the thing in its concreteness. 
The judgment that pronounces what is involved in this con- 
tent and what is not rests on the presumption of the indi- 
vidual unity of the content, and on the capacity of .discerning 
from the structure of this unity aided by empirical know- 
ledge of instances what is essential to it and in what degree. 
The insight in question has undoubtedly some kinship to 
aesthetic judgment, for both depend on the power of seizing 
the concretely presented import or principle of unity of a 
concrete whole. To judge the structure of a fossil creature 
from a vertebra, or to detect the affinity between two 
zoological species which are externally much modified, is a 
synthetic apprehension of the same nature as that which 
realises the construction of a picture or of a drama. Such 
judgment, however, is merely the condition precedent, and 
not the essence, of the true relation between the mind and 
fine art. 

The analogical judgment, like the aesthetic judgment, is 
essentially outside relativity and necessity, and incapable of 
being resolved into them. It is true that judgments of 
abstract relation, drawn from the mechanical or geometrical 
sciences, are perpetually coming in aid of analogical truth, 
by indicating that this or that de facto service within the 
concrete individual can only be performed by its parts 
under this or that condition. To support a certain weight 
the plant stem or spinal column must have adequate 
strength. To impel a certain bulk and mass through the 
air at a certain velocity the bird's wings must have a certain 
area and striking rate, the arrangements necessary to which 
of course react on the whole muscular circulatory and 

230 Singular and Universal Judgment. [bookI. 

respiratory apparatus. But even this merely rhetorical 
selection of an abstract final cause is really unjustifiable. 
Which comes first ? why such a weight on the stem ? 
why should the bird's body have such a bulk or mass? 
There is nothing to fix any one of these elements as a 
given final cause to which the others must be adapted. 
Adaptation to the bird's prey or the like is again simply 
de facto. An animal might have to change its prey by 
reason of a change in their relative powers, just as probably 
as it might develope new powers to keep pace with those of 
its prey. And further, in the background we may see such 
a law as that of the Conservation of Energy dominating the 
entire system and operations of everything that moves. 
In all these relations we observe the ultimate character of 
necessity, viz. the reference of a subject to a whole other 
than itself; e. g. the treatment of an animal as a part in the 
whole of moving matter, or as a figure having properties in 
space, so that in each of these relations it appears as deter- 
mined by the character of a totality other than its concrete 
self. The nature of space for instance is per se a datum 
or fact ; but when it determines the results entailed, e. g. by 
the shape of a leaf, it is exhibited as a whole prescribing 
the relation of its parts, which relation as regarding some- 
thing that is not merely a part in space is external but 
constraining and so necessary. 

Yet even if the entire construction of an individual con- 
tent were laid before us in terms of mechanical analysis, 
still the analogical judgment would force itself upon us, as 
the aesthetic judgment would in a parallel case. Analogy 
would then indeed no longer be the chief instrument in dis- 
covery, or at least in presumption of universal connections, 
because these would be capable of constructive apprehen- 
sion of a more direct and relevant kind. Such a state of 
knowledge may already in some degree be illustrated by 
the Darwinian analysis, say, of an orchid-blossom, in as far 
as it succeeds in tracing the mechanical modifications, 
which, each of them representing a definite physical adap- 

chap. v.] Individuality as a Result, 231 

tation to some external circumstance, have generated the 
present structure of the flower. The same observation might 
even be applied to the identification of types and their 
affinities. The. mechanical history of any organic structure 
would, if ideally complete, include the nature, degree and 
physical causes of its deviation from kindred structures. 

But all this would not interfere with the import of the 
generic or analogical judgment. For this import consists 
in the identification of individuals with a concrete content, 
and such an identification involves connections which 
differ in kind from the identification of abstract relations 
which are not Things. They take the content not in 
its external relativity, but in its relation to self or to an 
immanent final cause a final cause identical with itself. 
We have examined this self- relation in the more difficult 
case of geometrical figures which are absolutely and ade- 
quately reducible to examples of general conditions, and 
seem merely to mimic the self-contained relation of the 
concrete thing. This relation is an element of import 
which does not wholly disappear even in those kinds of 
existence which are hardly ranked by common language in 
the category of individual things as we saw to be the 
case e.g. with the elements, and in short with all un- 
organised substances. I do not restrict the meaning of the 
term unorganised to = ' inorganic ' in the technical sense ; 
but I employ it to designate any portion of matter, organic 
or inorganic, which is not shaped into a whole by human 
activity, or regarded in respect of its natural subordination 
of parts with interest due to its unity for our intelligence. 
Every element has no doubt its peculiar minute structure, 
and every fragment or portion of matter has no doubt its spa- 
tial or other relations which unite it into a whole. A pebble 
or a bit of rhomboidal spar or a nugget of gold has a self- 
relation, a characteristic peculiarity which makes it single, 
and distinguishes it as a persistent universal from things 
external to it. Much more has any organism a typical 
individuality which introduces the distinction of inner and 

232 Singular and Universal Judgment, [booki. 

outer, essential and relative, into what as a mere example 
of general laws has no self-relation 1 and no inner or outer. 
And in these last two sentences I have omitted the 
strongest case, because it is so strong as to dispense with 
the reservation which we were trying to illustrate. But 
when we come to reflect on the conception of a things we 
must be struck with the fact that by far the greater amount 
of what we most readily recognise under that title are ob- 
jects made by man for purposes which he consciously em- 
bodies in their structure. I cannot think that, apart from 
our familiarity with such objects, the conception of a thing 
would seem so simple as it does. A mountain, a waterfall, 
a wave of the sea, are things chiefly to the aesthetic percep- 
tion ; and if we left this perception out of account, it would 
not be easy to assign the boundaries of their individuality, 
or to single out its essence. Complaint has been made 2 
that those who lay stress on the progressive interpretation 
of the idea in nature do not find room in their theories 
for the achievements of the screw and the lever, and for 
the laws of the equilibrium of fluids, of pressure, and of 
tension. These examples may be regarded in two aspects. 
The screw and the lever are best known to us as tools, in 
which capacity they belong to the sphere of mind, as ob- 
jects endowed by human foresight with an immanent signi- 
ficance depending on their adaptation to a determinate 
purpose. But as mere characteristics of matter mechani- 
cally considered they rank with any of its general attri- 
butes, rigidity, gravity, inertia, attributes which are the 
basis of all material organisation, but do not by themselves 
suffice to give individual interest to any fragment in which 
they are embodied ; and among such attributes must be 
ranked equilibrium of fluids, and the effects of tension or 
of pressure. 

1 Of course such a point of view is unreal in its abstraction. If the thing 
were absolutely regarded without self-relation, its external relation would be 
gone too, for what would there be to determine it? The point is that the 
centre of interest, in relativity, falls outside the self. 

2 Lotze, Mikrokosmus, English Translation, vol. i. p. 17. 

chap, v.] Double Import of Mechanism. 233 

But what are we to say of the shell that screws itself into 
the sand, of the screw propulsion exerted by the porpoise's 
tail, or of the levers which form the limbs of animals ? We 
dare only speak, in relation to such phenomena, of a de facto 
purpose or actual function. In virtue of this function, this 
contribution to an obvious and real end, the total life and 
motion of the animal in which they are found, we claim for 
these arrangements a morphological unity which forces us 
to grant them the character of elements in things that have 
concrete individuality. We dare not ascribe to them the 
unity of an ideal purpose, as we safely may to the screw 
of a micrometer or to the lever of a balance ; but we treat 
them as elements in a unity analogous to that w T ith which 
we are familiar in objects that represent the purposes of 
our mind. The rudest mechanical contrivance is in this 
respect on a level with the products of fine art and superior 
to those of nature, that it unites the abstractness of thought 
with the concreteness of sensuous existence; i.e. while in 
one aspect a mere material object, yet in another it em- 
bodies an idea, and does so determinately and without 

Thus the conception of machinery has a double and 
not a single import for logic. If on the one hand it 
accents the fact that matter is indifferent to our purposes 
and simply acts and reacts according to its own nature 
and it is this of which we are constantly being reminded as 
the mechanical or uniform aspect of the world yet on the 
other hand it is the most obvious example of a concrete 
embodiment of mind in matter, and corroborates if it does 
not awaken the reflections of the understanding on the ra- 
tionality of things. Of this rationality the existence of in- 
dividual types as concrete universals recognisable by the 
analogical judgment is a higher phase, a phase more akin 
to individual intelligence, than matter in its abstract and 
general modes. And therefore the generic judgment rest- 
ing on analogy, i.e. on the perception of concrete identity 
of content, is not capable of being superseded by the ab- 

234 Singular and Universal Judgment, [booki. 

stract judgment of pure relativity. The latter, if ideally- 
complete, gives a true account of what occurs in terms of 
mass and motion, but necessarily omits the teleological or 
quasi-teleological import which gives the content of the 
judgment its interest and significance for knowledge. 

I will analyse a single example. Exogenous trees dis- 
play 'annual rings' in the wood, which are due to the aug- 
mented pressure of the bark as each year's new wood 
expands the stem, resulting in the flatter formation of the 
outer and later cells in every year 1 . As this stands I call 
it a generic or analogical judgment. It is indeed based on 
one of the above-mentioned simple mechanical relations, 
the effect of pressure ; but it predicates this relation with- 
in a concrete individuality which gives it an import that 
as a mere mechanical problem it would not possess. Let 
us reduce its essential points, however roughly, into the 
latter shape. We shall obtain some such residuum as this : 
'A fabric gradually constructed under increasing pressure 
out of a material which hardens after a time will show in- 
creasing effects of pressure in its later-formed portion.' 
Here we have, in part at least, ' freed the direction,' to borrow 
an expressive phrase from Bacon, i.e. stripped off circum- 
stances which are irrelevant to the production of the effect 
in question. But with these irrelevancies we have lost in the 
case before us not merely confused concomitants of percep- 
tion, but the interest which gave the example its place in 
knowledge. The fabric is no longer wood, the gradation 
no longer that displayed in the annual rings of timber, the 
subject of the judgment is no longer reality embodied in 
the characteristic individuality of the exogenous trees. The 
import of the judgment is gone. ' But its content is sub- 
sumed under the simple mechanical relation, if this is rightly 
understood.' Perhaps ; but what does this mean ? If the 
import of the concrete thought is to be saved, it must mean 

1 Probably other causes concur in this process. I have purposely simplified 
it. The rings are annual only if the period of growth in the year is single. 
A second hot season may cause a second ring. 

chap, v.] Distinction of Categories, 235 

that the analogical judgment is re-thought in its full depth, 
but with the explicit knowledge that it includes the abstract 
mechanical relation. The typical character of exogenous 
trees, though we must not call it a final cause, yet prescribes 
the extension and gives a definite reference to the content 
of the judgment. And I must here put the reader in mind, 
that, wishing to gain nothing from what may be called acci- 
dental ignorance, I have laid no stress on the present im- 
possibility of constructing any living thing on purely me- 
chanical principles. Individuality rests on a difference, not 
on a confusion, of categories. I am convinced that no 
organic nor spiritual movement accessible to human intel- 
ligence is without a mechanical aspect. I have therefore 
treated the present subject from a point of view which ad- 
mits, such an aspect to be knowable in all vital and spiritual 
processes. This point of view may seem absurdly fictitious 
when we consider the present state of exact explanation in 
the sphere of biology, or again of social science. The 
generic or analogical judgment now has, and seems likely 
long to retain, what we may describe as a secondary func- 
tion ; a function not merely of interpreting but of predicting 
not merely of resuming sensible facts under higher cate- 
gories, but of anticipating -their actual occurrence. In all 
science that deals with subjects beyond our power to con- 
struct, we draw our conclusions by means of analogical 
judgment in this secondary sense. When we judge a par- 
ticular plant of deadly nightshade to be poisonous, or a 
particular red stag to be dangerous at a certain time of 
year, we are judging on analogy ; on an anticipation based 
upon a concrete character whose particulars we cannot con- 
struct. The precise nature of these inferences will occupy 
us in the theory of inference ; it is plain that the larger part 
of inexact science consists of them. 

We must not confuse analogy in that secondary sense, 
as a mere anticipation of nature 1 , with the true generic or 
analogical judgment which is compatible with complete 

1 Anticipatio naturae. Bacon. 

236 Singular and Universal Judgment, [booki. 

analytic perception of mechanical cause and effect within 
the subject considered. We have perfect examples of these 
latter judgments in the case of things made by man for a 
purpose; in which a complete and accurate perception of 
their structure, interior causal nexus, and inevitable course 
of movement in no way supersedes the summary of their 
import which a knowledge of their purpose enables us to 
embody in a generic judgment. When we wind up a watch 
of which we know the construction, we do not merely an- 
ticipate that it will go because we have seen other watches 
go ; we can point to the specific causal connections by 
which it must (excluding accidents) result that the main- 
spring, unwinding itself, will draw round the wheels ; that 
the motion passed through the wheels will at one point be 
regulated by the escapement, &c, &o If we knew nothing 
of the use of a uniform measure of succession, but had 
some experience in mechanics, we should be quite certain 
that the watch must go, but we should have no notion of 
its generic content we should not know ' what a watch is,' 
i. e. what its purpose is. We could not therefore make the 
pure generic judgment, 'A watch is a motion regulated by 
an escapement so as to maintain a uniform rate.' In order 
to this judgment we must know the purpose of the instru- 
ment, viz. to maintain a uniform rate. With this know- 
ledge however we are in a position which, in strict theory, 
we can never attain with regard to any natural product. We 
can dictate the generic import of the watch ; we can say that 
if any watch possesses this import imperfectly it is a bad 
watch ; if it possesses it not at all, it is not a watch at all. 

Judgments such as this form the ideal to which the 
universal judgment in the form now under consideration 
always aspires. The properties expressed in such judg- 
ments are not merely anticipated or presumed; they are, 
or at least may be without altering the nature of the judg- 
ment, deducible with the utmost rigour. Yet, again, they 
are not mere causal sequences ; it is possible to have before 
us all the causal sequences concerned in the object, and yet 

chap, v.] Affirmation in Generic Judgment. 237 

not to make the true generic judgment which unites them 
into a coherent system. In this class of objects we may 
fearlessly say that it is the purpose which is the essence, 
and that generic, judgment rests on the knowledge of es- 
sence. In all other classes of objects such a view has degrees 
of precariousness, and can only be applied to the purpose 
as immanent, and therefore as not determinate, and as 
uncertain in its boundaries. Nevertheless, when we predi- 
cate in the organic world ' growth/ ' development,' ' self-pre- 
servation,' ' irritability,' we are really referring mechanical 
processes to an idea of life an idea of self-relation, of 'inner' 
and 'outer,' which is a higher result, though it is a result, of 
their purely mechanical nature. 

The above is the best account that I can give of the normal 
generic judgment, which represents the really central pheno- 
mena that were designated under the title of Universal Judg- 
ment by Formal Logic. The point of view which emerged 
in comparing this Universal with the Collective Judgment, 
and which was suggested by the quasi-collective form of the 
plural subject with ' All,' can never have been really felt to 
include what the judgment intended to affirm. But, as was 
said above, ' allness' is undoubtedly an aspect of universality. 

b. In order to bring to a focus the nature of this judg- Existential 
ment we have now to consider how its affirmation is to be meanln g- J 
classed whether as asserting the existence of fact, or the 
connection of attributes. 

To determine this question, we must recur to the distinc- t 
tion laid down above 1 between abstractness as a character of ( 
thought in contrast with sense-perception and abstractness 
as belonging to a kind of thought as distinguished from con- 
crete thought. Abstractness in the former sense is compatible 
with individuality, while in the latter sense it is not ; and it is 
in the former sense that we apply the term abstract to the 
ideas which are subjects in the generic judgment. Thus 
though we have no longer a proper name as in the singular 
judgment, yet we have a concrete idea, which being as a whole 

1 p. 228, supra. 

238 Singular and Universal Judgment, [booki. 

capable of reality, presupposes such a reality. We saw that 
in the case of the demonstratives 'This,' ' Here,' &c.the reality 
which is the immediate subject cannot be intelligibly taken 
as affirmed to exist, but only as presupposed. The ideal 
qualification which sometimes accompanies such demon- 
stratives showed us the point at which presupposition of 
existence tends to pass ,into affirmation, simply because a 
significant presupposition can be intelligibly denied. But 
this tendency is never absolutely fulfilled. The union of 
actual and ideal qualifications in the demonstrative judg- 
ment e. g. ' This bad man,' for though he were a good 
man he would still be this always leaves the ideal qualifi- 
cation the option of being read as a condition. The proper 
name, again, in its primary function, being void of deter- 
minate meaning, presupposes rather than affirms the exist- 
ence, of its content. It only tells you that some individual 
is in question ; and you cannot deny that an individual 
may be in question. But then as the proper name becomes 
more charged with import, which may even be made ex- 
plicit in ideal contents as it is in the Corporate Judgment, 
it also becomes as we saw capable of conditional meaning. 
Now as the primary function of the proper name can never 
be cancelled while it remains ' proper,' there arises within 
the singular judgment a parallel ambiguity to that which 
arises within the demonstrative judgment. The presupposi- 
tion that reference is in any case made to actual existence 
is at war with the determinate qualification which can and 
will only refer to some determinate existence that may or 
may not be forthcoming. A determinate, i. e. significant, 
ideal qualification standing as or in the subject of a judg- 
ment is never unambiguously affirmed to be an actual exist- 
ence. It may always take refuge in a conditional meaning. 
The reference to actual existence is presupposed in the sense 
possible for the subject \ in perceptive judgments because we 
are never without perception, and in singular judgments 
because the form of the subject-idea suggests an individual, 
and reality consists of individuals. 

chap, v.] Existential and Conditional. 239 

The independence of these two kinds of qualification, 
ideal and existential, and their consequent liability to con- 
tradict one another, is the very root both of existential and 
of conditional affirmation. In existential affirmation the 
two qualifications are taken as meant to coincide, though it 
is a purely material assumption or assertion that they do so ; 
in conditional affirmation the two are allowed to fall apart, 
i. e. the ideal qualification is not read as implying an indi- 
vidual reality that possesses it. 

Returning now to the concrete idea which stands as 
subject in the generic judgment, ' society,' ' man,' ' art,' ' the 
bird,' 'the rose,' 'a time-piece,' 'a telescope,' we find the same 
elements of meaning, but in reversed proportions. The 
subject here consists technically and primarily of ideal 
qualification and nothing more. It has reference neither to 
an unnamed perception nor to a unique individual undeter- 
mined by abstract significance. Hence the presupposition 
that the subject is an actual reality is less prominent, while 
the abstract conditional import of the ideal content is more 
so. In the earlier types of judgment we feel that we are 
referring to reality, and we assent with reluctance to the 
analysis which shows us that our reference is conditional. 
In the more abstract forms at any rate of the generic judg- 
ment we feel that we are affirming conditionally, and we at 
once acknowledge our reference to actual reality to be 
merely implied or presupposed. It will be noticed that I 
do not admit this side of the antithesis to be completely 
developed in the simpler generic judgments. I do not think 
that in ' The rose has pinnate leaves and perigynous 
flowers ' the existence of the subject is merely' implied ' and 
not * asserted.' It is not uncommon to find in a manual of 
botany ' Such and such a variety is no doubt a mistake of 
the observer,' which shows that the observer's description 
asserts existence so far as existence is asserted by any judg- 
ment l . All this however is a mere question of degree. What 

1 It may be said that in such a case the observer has alleged the plant to 
have been found in a given spot at a given time. But this is not essential ; he 
may simply send in the description. 

240 Singular and Universal Judgment, [bookt. 

I am here concerned to show is that the mere implication 
or presupposition of real existence, to which in one way or 
another we do undoubtedly come in the Universal Judg- 
ment, is not extraneous to the affirmation and dependent on 
a mere fancy or habit of ours, but is the lineal descendant, 
mutatis mutandis, of that so-called existential affirma- 
tion which we have traced in perception. and in narrative. 
And the strength of this implication depends on the con- 
creteness of the idea which here forms the immediate sub- 
ject in judgment. We have then here as before two 
elements in the content, or rather a content regarded in 
two lights. We have self-relation, existence, or a cate- 
gorical aspect, and external relation, necessity, or a hypo- 
thetical aspect. But the nature of the generic affirmation, 
as analysed above, shows for the first time a trace of recon- 
ciliation between these two points of view. The concrete 
self-relation is no longer void of meaning and purely desig- 
native ; it is a system of assignable import, and the analogy 
of which we have spoken is the anticipation or the insight 
based on this import. But again, this analogy introduces 
relativity and necessity, and as we saw interprets relations 
that unite the individuality in question with other totalities 
which prescribe to it either conditions or purposes. Thus 
the generic judgment is categorical in respect of its concrete 
self-relation, and hypothetical or necessary in respect of the 
analogical or constructive nexus to which the import of 
that self-relation gives rise. 

But, it will be objected, this might be all very well if we 
were speaking of individuals, whose nature is to be unique, 
like the present Queen of England, or the centre of the 
material universe ; but here we are speaking of an indefinite 
set or series of individuals whose common nature is nothing 
and nowhere but in them. This is, it may be urged, 
Scholastic Realism over again. What existence does a 
generic judgment presuppose, when and where? In reply 
to such an objection, I insist in the first place that we 
cannot treat any imperfection of knowledge as incident to 

chap, v.] Existence of a Kind. 241 

knowledge unless we can prove that it necessarily is so, and 
that to treat a natural kind as an indefinite set or series of 
individuals is an imperfection of knowledge which can be 
shown not to be necessary. This consideration however 
belongs to the subsequent section. 

But in the second place I reply that even without 
treating a kind as an actual unity, and though in fact we 
do not treat it so in judgments which are true of each 
individual singly (as common generic judgments are), yet 
still the individuality of the content dictates its own time, 
place and measure of existence. And it is this time, 
place and measure, wholly without reference to subjec- 
tive era *, place or fancy, that is affirmed 2 in generic 
judgment. It is characteristic of the rose to exist in a 
certain epoch of evolution and within certain limits on the 
earth's surface. Existence within this time and place, 
subject to such variation as the nature of the content 
allows, is what the generic judgment affirms (or implies) of 
the rose ; that is to say, in affirming that ' the rose has 
perigynous flowers ' we mean that individual actual roses, 
found within these limits, have the attribute in question. If 
there are none such, then the rose is like any genus or species 
that has been imagined to exist by a mistake of identifica- 
tion ; the kind in question would in that case not exist, and 
the judgment would beyond question be false. Of course 
in every-day subjective judging the place and time etc. of 
existence is but roughly indicated by what we happen to 
know or believe about the actual subject of judgment, but 
it is never referred to the time or place in which we judge, 
unless per accidens our knowledge is limited to, or the con- 
tent especially concerns, that time and place. Rose in the 

1 See above, p. 217, discussion on tense in judgment. 

2 I should not object to replacing ' affirmed ' by ' implied,' in order to mark 
the unquestioned line between the singular and the universal judgment, if it were 
admitted that the implication is an integral part of the judgment, and not a 
fancy of our own. The point is that existence is implied or affirmed in these 
judgments, just as Necessary connection is implied or affirmed in Perceptive and 
Singular judgments. 

VOL. I. R 

242 Singular and Universal Judgment, [book i. 

j abstract does not exist. But it is a concrete universal which 

has power, in the context of the real world to which we 
refer it, to dictate the epoch, place and quantity of its indi- 
te vidual embodiment. 

I need hardly guard myself against the misapprehension 
that I am alleging that anything and everything exists which 
we choose to fancy. I am maintaining just the opposite, 
viz. that if we attempt to embody fancied realities in judg- 
ment, such judgment is false ; for all judgment is a definition 
of real reality. We can only escape this result if the fancied 
content is such as is in its logical nature debarred from 
being real, i. e. a mere abstraction, and is therefore incapable 
of claiming to stand for a reality. 
Individual c. The reality involved in 'a concrete universal will be 
Judgment. ma de plain by insisting on a third aspect of the generic 
judgment, viz. that in which it challenges comparison with 
the Corporate Judgment. For this purpose we must think 
of generic judgments which are not merely analogical, but 
which for want of a better term I may designate as Indi- 
vidual. These judgments are characterised by not being 
true of any and every individual singly, but only of the 
kind taken as an individual. Such judgments are, ' The 
animal world represents an evolution coordinate with that 
of the plant world,' ' The Orchidean order includes 433 
genera and probably about 6000 species,' ' Space has 
three dimensions,' ' Humanity is the object of worship to 
Positivists,' ' Monarchy disappears with the advance of 

In comparing such judgments as the above with that 
form of the Singular Judgment which we called the Cor- 
porate Judgment, we find at first sight little distinction 
between them beyond the fact that these Generic Judg- 
ments do not employ a proper name in the subject, 
whereas the Corporate Judgments do. And even this 
distinction is in some degree bridged over when we call 
to mind that such determinations as ' now,' * last year,' 
* this,' and ' mine ' appeared to us essentially to rank either 

chap, v.] Proper Name and Generic Name. 243 

with proper names or with demonstratives ; and also that 
there is a tendency on the part of proper names themselves 
to assume abstract significance, so that a proper name is 
not always easily distinguished from a generic name. The 
Greek race, Europe, are proper names ; but it is more 
doubtful how we should class ' the Aryan languages,' ' the 
North Pole,' and ' the Mahometan religion.' Again, the 
earth,' 'the solar system,' seem free from all arbitrary 
reference ; but in speaking of them we really imply ' our 
earth,' ' our solar system,' and so fall back into some form 
of the singular judgment. 

The difficulty is worth noticing ; but it is simply one of 
those which must arise from the Sorites-like character of 
any continuous evolution. It is hard to say whether ' the 
Mahometan religion,' as we mean to employ the term, 
involves a reference strictly of the order of a proper name 1 , 
or on the other hand is simply an ideal content, and, so 
far as ideal, abstract. The reason of this is that the con- 
ception is in fact on the border-land between the proper 
name and the mere determinate content, and in all proba- 
bility it is sometimes employed in the one sense and some- 
times in the other. The question is whether the general 
meaning or the individual identification comes first in the 
mind. As we saw above, it is not improbable that in 
primitive careless and unscientific thought the significant 
word is not made distinct from the proper name in other 
words, the intension which is the mere means to identifi- 
cation is the only intension signified, but for this very 
reason the purpose of identification is not distinguished, 
so as to be considered primary, from the purpose of defini- 
tion. In fact, when we now speak colloquially of ' the bay 
mare,' ' the low pasture-field,' we are using ' bay ' and ' low ' 
merely as signs of identification, though of course by help 

1 In every case we must keep etymology out of the question. The reference 
to Mahomet as a historical individual is certainly not the chief element, and 
perhaps hardly an essential element at all, in the direct significance of 
1 Mahometan ' at the present day. Cp. the rhetorical antithesis that has been 
drawn between ' Christianity ' and ' the religion of Jesus.' 

R % 

244 Singular and Universal Judgment, [booki. 

of their meaning. Such is the type of usage which we may- 
imagine to have been the common root of the significant 
and the proper name. The terms of the Linnaean arrange- 
ment of plants, in as far as they are subservient to mere 
recognition, are a somewhat similar case in point. 

But when all deductions are made, there remains a clear 
distinction of principle between judgments which use proper 
names, and judgments which do not. From this point of 
view the generic judgments now before us agree with those 
last discussed and contrast with the singular judgment. 
They are able to convey their reference to reality by means 
of a determinate ideal content. 

On the other hand, in the nature of their reference to 
reality they agree with the singular judgment and differ 
from the common generic judgment. They do not rest on 
analogy. The individual to which they refer is a real and 
a single individual, and not a mere individuality. So far 
from being mediated predications about a number of 
particulars they are not even true of the particulars that 
enter into their content. When we said, in the former 
section, ' The rose has perigynous flowers,' we were treating 
the individuality of all roses as one by analogy 1 . But 
when we say, ' The rose family is a descendant of x> a diver- 
gence from y, and a transition towards #,' such a judgment 
is not made about each particular plant within the tribe, 
nor even about each particular species. If true, it is true 
of the whole section of plant-life in which every particular 
rose-plant is a distinct and separate progressive or diver- 
gent phase. There can be no doubt, I think, that from 

1 Subtlety of transition must have an end somewhere in writing, but in fact 
it has none. Thus the reader may object that if it is nonsense to say that the 
rose family as an actual individual has perigynous flowers, yet we may always 
safely say in such a case that it prescribes that the particular rose shall have 
perigynous flowers. I can only admit the objection ; the fact is so if we are 
bona fide regarding the genus as a whole of evolution, whose actual individu- 
ality expresses itself in this and in olher common predicates. But if as is most 
probable we realise nothing of the kind, but are merely going by analogy to a 
common property of roses, then we are treating the kind as a mere individuality, 
and must not pretend to be treating it as an individual. 

chap, v.] Generic as Categorical. 245 

an ideal point of view every natural kind in the concrete 
sensible world must be thus regarded ; and of course when 
we consider existences in which Intelligence is more 
definitely active society, mankind or at least civilised 
man, fine art, or morality in these phenomena the totality 
is more real and concrete, and the reciprocal relations of 
its parts exist not merely for the microscope of analysis, 
but as patent every-day facts. 

Although universal, the Generic judgment in the aspect 
now before us is fully Categorical. It is in this respect 
wholly on a level with the Singular judgment, being in fact 
related to the judgment of Analogy with its dual nature 
much as the Singular judgment is related to the propor- 
tional or comparative judgments that are introduced by a 
demonstrative. The Singular judgment may be regarded 
as a premature attempt to concentrate individuality the 
'characteristic quality' which the proportional judgment 
had revealed into an individual ; resulting as we saw in 
the omission of determinate quality from the individual 
content by the use of Proper Names. The generic judg- 
ment raises (in its Analogical form) and meets (in its Indi- 
vidual form) the same problem in a more adequate way, 
concentrating individuality into an individual by comple- 
tion and not by omission. It is as a system of such indi- 
viduals, united perhaps in a yet more concrete individual 
reality, that we must conceive of the world known to us 
through space and time, if we are to assign it any existence 
beyond the present of presentation. For us, it is plain, such 
individuals are intellectual constructions, and only attached 
to, not shut up within, the actual present perception. The 
distinction between concrete realities and abstract truths is 
not, for us at any rate, that the latter are intellectually 
initiated and the former are not ; it is not a question of 
origin, but a question of nature, i. e. of the degree in which 
a content is capable of being regarded as something that 
exists as a whole and can be considered in relation to itself, 
or on the other hand is incapable of being given as a whole 

246 Singular and Universal Judgment, [booki. 

and affords no matter for consideration in relation to itself. 
All contents must theoretically be regarded as combining 
these two characters ; and as an important application of 
this idea I may instance the answer to a question which 
arises when we make the categorical nature of assertion 
depend upon the degree of concrete self-relation. 

Is it possible, we shall be asked, to lay down a hard and 
fast line, by which abstract shall be divided from concrete 
contents ? And if not, does not our view surrender the self- 
dependence of reality and make it purely relative to fancies 
and notions in the individual mind ? Does it not enable us 
to treat as actual any content however abstract or trivial, 
and any however concrete or significant as a mere element 
in hypothesis, simply by varying the point of view from 
which we regard them ? And the answer is, that as reality 
unites these two characteristics, we can always emphasise 
either at will ; and further, we commit no error in so doing, 
unless we assume and assert the relation which we happen 
to be considering to be the only relation that there is. Our 
knowledge always falls short of reality, and apart from false 
identification of relations with which false antithesis is at 
bottom the same we have a right to see all that we can 
either of absoluteness or of relativity in any content what- 
ever. Reality is such that any element or feature of it, 
however slight or superficial, can be raised by our intellec- 
tual gaze to the position of a self- related significant whole. 
The nature of mind is present in everything; the only 
difficulty is to see it there. And such an elevation is not 
false, except in as far as it is exceptional ; in as far, that is, 
as we fail to view the remaining contents of reality with the 
same constructive insight. Not merely a fragment of stone 
or metal, but a colour, a curve, a relation of size or weight, 
is ideally capable of being passed through the stages of 
generic judgment, of being regarded first as an individuality, 
and then as an individual. What is false or forced in such 
a mode of contemplation depends on the want of proportion 
between it and our ordinary careless vision of organisms 

Chap, v.] Logic and Metaphysics. 247 

and fine art, of men and of society. All contents are rela- 
tive except the absolute ; but the import and degree of their 
relativity is not the same. 

A further corollary may be worth drawing in a few words 
from the above considerations. Our present treatment of 
logic starts from the individual mind, as that within which 
we have the actual facts of intelligence which we are 
attempting to interpret into a system. But our consequent 
preoccupation with the phenomena of the individual mind, 
with its imperfect grasp of reality and the varying aims and 
tendencies of its thought, brings with it a double danger 
which haunts every phrase and every idea in a logical 
treatise. Either one may speak as if reality were simply 
relative to the individual mind, a ridiculous idea, but one 
which the very caution required of a modern writer is apt 
to encourage ; for he hardly dares to allude to Mind as such 
or in itself; or one may become interested in tracing the 
germination and growth of ideas in the individual mind as 
typical facts indeed, but only as one animal's habits are 
typical of those of others, and so we may slur over the 
primary basis of logic, which is its relation to reality. For 
mental facts unrelated to Reality are not knowledge, and 
therefore have no place in Logic. The difficulty is, in other 
words, simply that modern Logic has a hard task to hold its 
own between Metaphysics and Psychology. I entertain no 
doubt that in content Logic is one with Metaphysics, and 
differs if at all simply in mode of treatment in tracing the 
evolution of knowledge in the light of its value and import, 
instead of attempting to summarise its value and import 
apart from the details of its evolution. My object however 
in mentioning the difficulty at this point is merely to protest 
that though I assume reality as the norm of the mind, in 
constructing which it is reconstructing and not creating de 
novo out of itself, yet I can entertain no doubt that intelli- 
gence is essential to the being of Reality, and that an 
abstraction which tries to regard the one apart from the 
other is a hopeless and helpless self-contradiction. As a 

248 Singular and Universal Judgment. 

I working conception in Logic we are forced to adopt some 
such idea as that of a normal intelligence operative in all 
human minds, but subject to the accidental limitations of 
each. The evolution of knowledge is, as Plato long ago 
portrayed it, the emancipation of individual minds from their 
accidental limitations, and their education into the knowledge 
of the one real and intelligible world. But the duty of 
modern science is to preserve the continuity of this evolu- 
tion, and to admit no saltus at any point between the world 
in which we live and the world which is real and intelligible. 
And in this continuity we have a standpoint which Plato, 
although he reached it, did not consistently maintain. 
Objective Intelligence presents itself in Logic as the mere 
postulate required by such a continuity, and, starting as we 
have done from the individual consciousness in time, it is 
merely as a postulate that we propose to treat it. To say 
that the real world is the intelligible world is only to repeat 
what we found ourselves obliged to suggest as an elucida- 
tion of the earlier stages of judgment, that reality is some- 
thing at which we arrive by a constructive process l . 

We are now to consider the consequence of emphasising 
the abstract or relative aspect of the Analogical judgment. 
We are thus led to a form of thought which is antithetical 
to the Individual Generic judgment of which we have just 
been speaking, and consequently must be regarded as a 
divergence from the concrete evolution of thought towards 
the mechanical or analytic judgments which begin with 

1 See above, Introduction, p. 41 ff. 


Universal Judgment {continued). 

ii. The Universal Judgment, when pushed to the extreme p ure Hypo- 
point of abstraction, becomes the Hypothetical Judgment, ^etical ~ 

a. The Hypothetical Judgment is distinguished from all Its relation 
which have thus far been spoken of, by its essentially abstract to previous 
character ; abstract not merely as thought is said to be 
abstract when compared with sense-perception, but as the 
thought of an ideally isolated attribute is abstract compared 
with the thought of a self-dependent and self-related in- 
dividual. It represents the fourth of the elements or 
aspects which have been confounded, or at any rate have not 
been duly distinguished, by traditional logic within the so- 
called Universal Judgment. Its differentia is that it does 
not refer to a concrete subject, not even to what we called 
an individuality or the concrete self-related content in its 
aspect of self-relatedness ; and that consequently we do not 
consider whether its subject is given in actuality or not. 
For it is essentially the judgment of necessity or relativity, 
in which the subject is taken, not given, and taken not for 
its own sake nor with reference to its individuality, but for 
the sake of that which is to follow from it, that is, for the 
sake of its relativity. It is a judgment which follows out 
the single thread of a nexus of attributes, and does not heed 
the import of the pattern into which it enters. If a 
gravitating body is set free to fall, it falls with an accelera- 
tion proportional to the squares of the times, whether it is 
a drop of rain, or a tortoise with the head of Aeschylus 
below it. Here we have, in an explicit shape, the relativity 
of knowledge which has haunted us throughout the evolu- 
tion of judgment, forbidding us to feel satisfied in connecting 

250 Universal Judgment. [booki. 

together any data which we might merely chance to light 
upon in conjunction, and requiring that every idea should 
always be limited and controlled by its reference to some- 
thing else, and not simply taken as we find it in perception 
or in ordinary life. And just because this principle has so 
haunted us, the judgment that embodies it cannot be 
sharply severed in meaning from the earlier forms of the 
universal judgment, and even the quasi-collective 'All 
gravitating bodies etc' may, and most frequently in this 
case does, contain what is really meant as a hypothetical 
affirmation. ' In this easel for the distinction really goes, as 
we have maintained all through, not by the shape of the 
proposition, but by the content of the judgment. The con- 
nection however between all the types of universal judg- 
ment is intimate and essential, so that in popular usage one 
easily slides into the other, or even combines the other 
with itself as its ground or consequence. When I say ' All 
animals need food ' I am probably expressing a quasi-col- 
lective conclusion about a property shared by all species of 
animals, taking its significance from an analogical perception 
of the generic function and immanent purpose of animal 
life, but ultimately resting on the hypothetical judgment ^ 
expressing a necessary or relative principle, ' If force is to be 
expended it must be supplied.' It will be observed that 
the second type of generic judgment, which for want of a 
better name I have called Individual Generic, is omitted 
from this combination of aspects. It represents a tendency 
divergent from that of the Hypothetical assertion, while 
the Analogical judgment is undecided between the two. 
If the Individual Generic judgment is capable of combina- 
tion with the Hypothetical, we must look for the result in 
the Disjunctive and not in the Universal affirmation. 
External (3. The type of the Hypothetical Judgment in traditional 
logic, so far as it is recognised at all, is stated in one of 
three forms: ' If A is B is;' 'If A is B, then C is D; 5 and 
' If A is B, then it is C The third of these forms is that 
which guides us to the true import of the judgment, though 


chap. vi.] Expression of Nextcs. 251 

conformably to the habitual irrelevancy of popular thought 
the second is that most commonly in use. But this second 
is obviously a broken-backed sequence, in which no point of 
unity is formally recognised between the antecedent and 
the consequent. When, indeed, significant words are sub- 
stituted for letters, the unity would generally be obvious, 
supposing the sequence to have scientific value at all ; but 
in such a case the expression is not essentially distinguish- 
able from that of the third form. The first form, ' If A is 
then B is,' has been said to be an abbreviation in which 
letters stand for clauses ; in that sense of course it must be 
reducible to either the second or the third form. We get 
the same result if we try to take it as a combination of 
single-word or impersonal predications. Contents may un- 
doubtedly be ascribed in judgment to an unanalysed 
present, but an unanalysed present can form no bond of 
union for a necessary sequence. ' If guilty, then death' is 
a mere linguistic abbreviation for ' If he is guilty then he 
will be put to death.' And even ' Where there is smoke, 
there is fire ' superadds to the impersonal ' There is ' a true 
local particle in the 'where' of the antecedent, and this 
reacts by a curious equivocation on the impersonal ' there ' 
of the consequent. No doubt, but for the awkwardness of 
the expression, we should say, ' Where there is smoke, 
there there is fire.' Here again, then, we have in essential 
meaning the third type of the Hypothetical judgment, 
1 If A is B, it (A) is C I will next illustrate the trans- 
formation of type ii. into type iii. ' If the barometer (A) 
falls (B), the weather (C) becomes stormy (D)'. 'If the 
atmosphere (A) decreases its pressure locally (B), it (A) 
must leave a gradient for wind (C).' But now if we take 
the lines, 

1 . . . when in Salamanca's cave 
Him listed his magic wand to wave, 
The bells would ring in Notre Dame,' 

we find that the saltus from antecedent to consequent is all 
but essential to the judgment ; the point of the mystery is 
that we cannot get at the underlying unity. Thus we see 

252 Universal Judgment. [Booki. 

the extreme case of type ii. in a judgment which has for its 
object to assert magical, i. e. irrational, connection. Of 
course the general scheme of reduction would have to be, 
' When his magical power (A) was exerted (B), it (A) could 
act at any distance (C).' It is in this sense that Schopenhauer 
calls some of Euclid's demonstrations conjuring tricks, 
because, although in a demonstration some unity of course 
must be shown between antecedent and consequent, yet 
the unity shown is often not central or fundamental \ and 
is therefore a causa cognoscendi, and not a causa essendi. 
In the pure type, ' If A is B, then C is D/ we have no indi- 
cation even of a causa cognoscendi. 

Much more might be said about the forms of conditional 
sentence ; but the subject is really grammatical rather than 
logical, for the hypothetical judgment can be expressed 
without a conditional sentence at all. Hypothetical and 
Categorical Judgment, as we understand the terms, are 
a question of content, not of grammatical form, and the 
hypothetical judgment is found wherever we frame asser- 
tions about an abstract content, in the above sense of 
abstractness ; although there is a difference of adequacy in 
different grammatical expressions for any kind of judgment, 
and the conditional sentence resists any attempt to embody 
in it a purely categorical meaning. ' If this man dies, our 
cause is lost,' takes ' this ' as a sign of unanalysed content 
and not as a point of attachment in reality. We know 
that the reason is somewhere in the unanalysed content, 
and so take it as an antecedent in the lump 2 . 
Assertion y. What is the precise nature of the assertion conveyed 
Hypotheti- by a Hypothetical Judgment ? In answer to this question 
caijudg- j shall speak first of the idea of Ground or nexus in 

ment. y 

general, secondly of Ground as compared with Cause, and 
thirdly illustrate our view by the attitude of the individual 
mind in hypothesis or supposition. 

1 Schopenhauer, Werke, i. 1 36 ff. 

2 I take this analysis, which appears to me exceedingly felicitous, from 
Bradley's Principles of Logic, pp. 89-90. 

chap. vi.] Ground as Identity in System. 253 

a. The contrast which we have anticipated throughout The idea of 
the above account of judgment determines the central Groun 
attribute which we are now to consider. The content of 
a true hypothetical judgment is abstract ; abstract in itself 
and not merely by the absence of sensuous perception. 
In other words, the subject of a hypothetical judgment 
is not an individual, not a whole, nor anything considered as 
a whole, i.e. as a self-related system. On the contrary, the 
content of a hypothetical judgment is composed of ground 
and consequent, each referring to something other than itself, 
and hence essentially a part. For a system as a whole, 
such as space, or the totality of gravitating matter, or the 
British Constitution, is a mere fact, complete in itself, and 
neither a ground for nor a conclusion from anything else 1 . It 
is only as parts within a system that elements can be so 
relative to one another that 'if this is so, then that must be so* 

It is only a question of detail how far the system in and 
by which the nexus subsists, is itself made explicit as 
a content within the hypothetical judgment. We may 
say, if we like, that the ideal of logical sequence demands 
that the system as a totality should be so made explicit, 
because the system is the real ground of the nexus ; and if 
the system does not appear in the content, the real ground 
does not appear in the content. But this argument, from 
the comprehensiveness of the real ground, does not overcome 
the essential principle which is involved in there being 
a ground, as ground, at all. Ground implies a consequent 
other than, though fundamentally one with, itself. This 
transition or otherness ceases to exist if the content does 
not formally present itself as part to part. For say that 
the totality of the system is explicit in the ground, still 
this totality is depressed into the relation of a part by 
the fact that a part is selected to appear over again as 

1 This applies to the examples given only when considered with reference to 
their internal nature. It may be said that space implies an intelligence ; but this 
is as within a further whole. There is of course no ultimately Absolute whole 
except the Absolute whole. 

254 Universal Judgment, [booki. 

consequent, and so as formally at least external to the 
ground. Thus it remains true that the elements of content 
in a hypothetical judgment are related as other to other 
within an identity which determines the one on the basis 
of the other. Such an identity, as far as exhibited in the 
one term that, in virtue of it, determines the other, is what 
we mean by Ground. It is obviously capable of all degrees 
of completeness up to the ultimate fact or whole which 
embraces in itself as parts both ground and consequent 
commonly so called. The various degrees of imperfection 
or broken-backedness in Hypothetical judgments, such for 
instance as were illustrated in the last section, are simply 
the degrees in which the system that determines the nexus 
fails to manifest itself within the content connected. It 
must not be forgotten however that we have refused to 
treat the grammatical form of propositions as decisive of 
the character of judgments. Where no rational nexus 
is traceable, but only a coincidence in fact, however 
general, we cannot admit that the essentials of hypothetical 
judgment are present. But then if we are impelled to 
make a judgment in hypothetical form, there always is 
some presumption of a rational nexus. We shall consider 
in the following section what attributes of true hypothetical 
judgments are shared by analogical assertions such as ' If he 
is a negro, he has woolly hair/ It is not worth while to 
insist more fully on these degrees of imperfection, except 
in so far as they will come under our notice in dealing with 
the doctrine of causation and with the kindred subject of 
the negative in hypothetical judgment. 

Let us attempt to make perfectly clear, before we go 
further, the nature of the relativity within a system which 
we ascribe to the contents before us. The simplest cases 
of such relativity are drawn from the field of numerical 
or geometrical construction. A Chinese puzzle or dissected 
map may give us a first idea. Any selected piece out of 
such an arrangement determines nothing by itself, but 
when a second piece is given some relation between them 

chap. vi.] The Basis of Necessity. 255 

emerges, though perhaps only a negative one. It is fur- 
ther possible for a piece entirely enclosed by others to 
have its place relatively to them determined long before 
the whole arrangement is completed; but this determi- 
nation will really be partial, for the place of the whole 
group of pieces cannot be determined till the whole puzzle 
is put together. Now the arrangement as a whole is a 
mere matter of fact ; it is only within it and by reason of it 
that each piece has a prescribed place in virtue of its own 
shape combined with the shapes of all the other pieces. 
All the pieces being given, of course the arrangement is given 
too ; but if nothing is given, of course all is in the air, and one 
arrangement and set of shapes is as likely as another. 

Or again in the region of number, we may take as equi- 
valent to Hypothetical judgments those which in treating 
of Enumeration we called Mediate. 50 x 3 = 25 x 6 would 
run in conditional language, ' If 50 is multiplied by 3, the 
product is equal to,' etc. Here we have one form of the 
numerical whole 150 presented as a term from which 
another term, viz. another form of the same whole, may 
be inferred. The system within which the relation exists 
is of course not the whole 150, but the system of number 
as such ; or we may say if we prefer, the whole 150 as 
involving and exemplifying the nature of the whole of 
number as such. This system may be brought to bear 
either by simple counting, the process which is so to speak 
the medium in which number exists ; or by developing any 
of the relations which are embodied in the several places of 
the series with their individual names. Thus the above 
statement may at once be reduced to a tautology by 
taking 50 as 25 x 1 and 6 as 2x3. The combinations 
which might be made with the same result might be 
pursued as long as we cared to continue the enumeration 
of places in the series, and from whatever point we started 
in the system we should obtain the same result so long as 
both sides of the equation were subjected to treatment that 
was equivalent according to the rules of the system. On 

256 Universal Judgment. [booki. 

the other hand, if we were to assume the invalidity of the 
equation, we should at once make the whole numerical 
system inconceivable a unit, say, would have to be 
taken as varying in value without being subjected to 
any arithmetical process, and such variation is incom- 
patible with the fundamental principle of number. 

The same may be shown in space, treating it not qua 
extended whole of parts outside one another, but in respect 
of the connection of its attributes. ' If two straight lines 
have the same direction, they can never meet.' This is 
a consequence drawn from the conception of direction in 
homogeneous space. If we destroy the idea of homogeneous 
space, the relation, which only holds within a totality having 
that attribute, is annihilated. If there can be a change of 
direction which yet is not a change of direction I do not 
know how else to express the notion of direction in space 
which is itself curved then, I presume, the judgment from 
which we started is no longer true. 

The same characteristic might be pointed out in relation 
to gravity, inertia, or any property which is the basis of 
exact inference. The consequences of gravity hold only 
within the totality of gravitating matter, of inertia in the 
combination of motions, and so forth. Every sphere of 
this kind, every set of relations within which certain nexus 
of attributes hold good, is itself ultimately a fact or datum, 
relative no doubt within some further totality, but absolute 
relatively to the inferences drawn within it. Hence we are 
brought to a conclusion of the last importance. All hypo- 
thetical judgment rests on a categorical basis. That is to 
say, all relativity rests on an absolute datum and all ne- 
cessity on fact. Why then is mechanism, necessity or 
relativity, opposed to individuality, fact or absoluteness, if 
all mechanical relations are themselves characteristics given 
in some individual whole 1 ? The answer seems to be dic- 

1 Space and Time are as we saw imperfect individualities. But it is their 
individuality and not their imperfection that makes them sources of general 
relations in things. 

chap, vi.] Examples of Necessity. 257 

tated by what has been said. Individuality is in self-rela- 
tion, Necessity is in external relation. But as all relation 
is within some whole, it follows that wherever we have 
necessity or relativity we are concerned with more than 
one whole or individual content ; that is to say, we have 
a whole or content with its own import and significance 
taken as a part within a wider or completer totality 1 . 
The ground or necessity which forms the affirmed nexus 
of attributes lies then in the systematic nature of the wider 
whole, that within which the terms of the nexus are capable 
of being opposed as part to part. 

We will examine two or three instances of ground and 
consequent in the light of the above doctrine. ' A picture 
6 ft. x 7 ft. cannot be hung in a space 5 ft. x 6 ft.' Here 
we are taking the picture as a whole in itself, but as a part 
within space, and as therefore having external relations de- 
termined by the spatial system as including other objects. 
The arrangement of other spatial objects so as to leave only 
the area 5 ft. x 6 ft. is incompatible with the occupation of 
the area 6 ft. x 7 ft. by the picture. But again, we may 
judge that 'If the boat in the right foreground of the pic- 
ture were erased, the arrangement of the distances would 
become confused.' In this judgment we still call attention 
to spatial determinations, but only as involved in the con- 
crete individuality of the work of art, which assigns them 
their meaning and value. We are thus taking not space as 
such, but the individual picture before us, as the totality or 
determining system, and contemplating the necessary rela- 
tions which this fact or whole, from its nature and structure, 
imposes on its several parts. Of course, apart from the 
effect of the whole picture, there would be no such necessity 
or relation between the parts. This is an illustration of the 
ultimate nature of logical necessity or relativity and its re- 
lation to fact, which is, if not specially felicitous, at least 
true in every detail. In a true work of art we have the 
bearing of every part on every other, the innumerable de- 

1 See on Measurement, chap, iii, supra. 
VOL. I. S 

258 Universal Judgment, [booki. 

tails, none of which could be altered without necessitating 
the alteration of others, all concentrated in a unity which 
is itself constituted by all these parts, and yet, as a whole, 
prescribes the relations existing between them. And yet 
the whole is itself a comprehensive fact, and apart from it 
or outside it all these prescribed relations lose their neces- 
sity and disappear. 

Again, take such a judgment as 'The sound of the violin 
is of peculiarly piercing quality.' If we describe the sound 
merely in terms of the mechanical system of vibratory 
movements, it is governed by the necessary relation, ' If 
a string be dragged by a bow, slipping from it at in- 
tervals, its vibration is of highly angular form,' i. e. in terms 
of its effect on the air, produces sharp and not gradual 
transitions from increase to decrease of condensation. Omit- 
ting the effect on our hearing, this is a nexus of attributes 
grounded in the properties of vibrating bodies, and in the laws 
of friction and of undulatory transmission. But here again the 
whole system of physical properties, though comprehensive, 
is a datum, and except in it no necessity could be shown 
why motion communicated by a bow must have this parti- 
cular form, or why this particular form should find a cor- 
relative in a peculiar type of impulse communicated to the 
air. It is this system which as an identity in differences 
appears first in the effect of the bow on the string, and 
then in the peculiar impulses communicated to the air by 
the sounding-board. It is only as having such a unity 
behind both of them that the one of these phenomena can 
condition the other. And here again we may obtain a re- 
lative absolute by considering the compound tone of the 
violin string as perceived by the mind through the ear, 
simply on its own merits. It then becomes an ultimate 
fact, embodying certain relations between musical sounds. 
And within this fact we may distinguish the necessary re- 
lation, ' When a tone is piercing in quality, the higher over- 
tones are strongly marked in it.' And finally, we may 
bring the physical and the musical system together under 

chap. vi.] Can the whole change? 259 

the complex fact of the correspondence between the shape 
of oscillations and the character of tones, and say on the 
faith of this complex fact that where the oscillations are 
angular, the higher overtones are audible, and proceed to 
the whole system of deductions made possible by Fourier's 
analysis of all vibrations into combined single oscillations. 

The idea on which we have been insisting that of a 
system or unity which prescribes the relation between its 
parts or differences is the idea of Ground, which includes 
the sphere of the Hypothetical Judgment, and indeed wher- 
ever it appears may be said to involve a Hypothetical ele- 
ment. It is difficult to express the essence of this concep- 
tion otherwise than by saying that the system is the same 
in the one difference or aspect as it is in the other. We 
thus appeal to the notion of identity in difference, which 
we have taken throughout to be the content of judgment. 
Only, as Ground, it is not mere identity, but systematic 
Identity, a notion easier to illustrate than to define, but 
apparently equivalent to { identity such that the differences 
in which it is manifested have definite relations to one an- 
other.' Of course any such definition only repeats the cha- 
racteristic which the account of the Hypothetical Judgment 

Assuming however these characteristics as summarised 
in the above definition, we can draw from them two con- 
sequences that affect the idea of Ground. First, it is plain 
that when once a Ground is rightly stated, in conformity 
with the true nature of the system which it presupposes, 
and with which it is in fact identical, such a Ground is un- 
alterable except by alteration of this system itself. With 
what justification, theoretically, we refuse to contemplate 
such alteration of the universe as a whole, or how far prac- 
tically we permit ourselves to contemplate it in respect of 
subordinate systems, e. g. man's moral nature or the type of 
disease, are questions that must be reserved for a general 
discussion of the postulates of knowledge. Formally, we 
may say, the whole cannot alter, because any alteration 

S % 

260 Universal Judgment. [booki. 

must be included in the whole. But we shall see that so 
purely formal a postulate would not satisfy the purposes 
for which a postulate is required. 

And secondly, it is plain that a ground is not rightly 
stated unless it either embodies the whole essence of the 
system which constitutes the ground, or at least is exactly 
relevant to or compatible with that system, and to the 
particular bearing which a given interest in any context 
imposes upon it. In the former case it is clear from what 
has been said that the hypothetical judgment must tend 
to expand itself into a categorical one. When we go to 
the root e.g. of geometrical truths we find ourselves affirm- 
ing facts regarding the nature of space. We shall thus at 
a later stage have to face the conception of judgments at 
once categorical and necessary; we have indeed anticipated 
something of the kind in speaking of the individual generic 
judgments. The latter case is that which gives rise to 
hypothetical judgments having strict reference to a sys- 
tematic ground, which they therefore imply, but do not 
need to express. Such are the ordinary statements of 
1 pure cases' in exact science, or geometrical truths as com- 
monly treated without raising fundamental questions of the 
nature of space. A ' pure case ' is a nexus of differences 
reduced to their expression as the differences of the system 
in which they have their nexus. Without knowledge of 
such a system we may analyse ad infinitum and yet never 
be sure that we have obtained a ' pure case.' This has, as 
we shall see, an important bearing on the theory of Induc- 
tion. I gave a rough instance of a pure case on p. 234 in 
reference to the annual rings of exogenous trees. Such, 
again, are the mechanical and chemical elements in the 
vital processes of man, e.g. the pumping action of the heart, 
the oxidation of the carbon in the blood and so forth, in 
stating any one of which as a necessary sequence of ground 
and consequent it must be treated as belonging to its own 
mechanical or chemical world, and not as an element in 
human life. All such judgments are abstract in the fullest Hypothetical is reciprocal, 261 

sense, and analytic ; their very point is that they disregard 
the import which constitutes the individual. On the other 
hand, a system which is the combination of individuals in 
their full import, i.e. the state in relation to moral beings 
within it, is most naturally dealt with not in hypothetical 
but in categorical judgments. For the subject is either the 
concrete system itself, or an individuality subordinate to it, 
taken in its full concreteness. It would be sheer pedantry 
to speak in hypothetical language of man's moral being, its 
ground, and its necessary relations. 

It is a corollary from the idea of Ground as a relation 
purely relevant to a positive determinate system that the 
hypothetical judgment, when ideally complete, must be a 
reciprocal judgment. ' If A is B, it is C must justify the 
inference ' If A is C, it is B.' We are of course in the 
habit of dealing with hypothetical judgments which will not 
admit of any such conversion, and the rules of logic accept 
this limitation as they accept the custom of ordinary speech 
as to the comparative range of subject and predication. 
Some cases of non-reciprocal sequence and their justifica- 
tion will be considered in the next section. But here we 
are only concerned to explain the principle upon which 
necessary sequence must ultimately rest ; and according to 
that principle, the unity of a system in its determinations, 
it follows that if A B necessitates A C, then A C must also 
necessitate A B. We are not now speaking of causation, 
but simply of coherence in principle, and it is obvious that 
the idea of coherence in a system is reciprocal. A cannot 
cohere with B unless B coheres with A. If in actual fact 
this is found not to hold good, and A B is found to involve 
A C while A C does not involve A B, it is plain that what 
was relevant to A C was not really A B but some element 
a ft within it. ' But may not the irrelevant element be just 
the element which made A B into A B as distinct from A C, 
so that by abstracting from it A B is reduced to A C, and 
the judgment is made a tautology, i.e. destroyed?' The 
suggestion is tempting, because it aims at cutting up by the 


262 Universal Judgment. [booki. 

root a troublesome scientific problem, viz. the statement of 
connected attributes as purely relevant to one another and 
yet as distinct. We constantly tend either to insert irrele- 
vancies by way of distinction, or to let both attributes fall 
back into the undistinguished abstract relation which con- 
nects them. To grasp a distinction in unity is an effort, 
and we dislike effort. Nevertheless, if it were impossible, 
the idea of system, of the one in the many, would be gone. 
A systematic relation is always within an individual whole, 
and the priority or antecedence of its elements belongs to 
the imperfection of knowledge, and not to the relation in 
itself. I am not saying that every individual reality exists 
endlessly in time, but I am saying that every whole in as far 
as its parts form a system has a nature which is independent 
of time, or (what really comes to the same thing) continues 
positively and actively through the fugitive moments of time. 
But apart from time on the one hand and irrelevant 
elements on the other, I cannot see how the relation of 
conditioning differs from that of being conditioned. Every 
B that is conditioned by A is the condition of A being such 
as to condition B, i. e. of A being what A is ; and if the 
being of A were wholly relevant to B, this would be equiva- 
lent to saying that the existence of B involves the existence 
of A. In other words, if there is nothing in A beyond what 
is necessary to B, then B involves A just as much as A in- 
volves B. But if A contains irrelevant elements, then of 
course the relation becomes one-sided, as if we were to say 
that a plane section of a sphere has its radii equal. The 
mention of the sphere makes the relation of coherence one- 
sided ; the circle need not be regarded as a section of a 
sphere. But, always assuming the homogeneous nature of 
Space, the relation between equidistance from a central 
point and uniformity of curve is inseparable, and it is 
impossible to see that either of these essential differences 
of the circle is prior to the other. It may however be 
questioned whether in an ultimate sense any incomplete 
case can be pure, i. e. whether irrelevancy can be wholly 


chap, vi.] Irrelevance hinders Reciprocity. 263 

avoided except by including the whole fact to which the 
judgment belongs. What, e. g. has distance to do with cur- 
vature ? The only answer is in the nature of space. This 
amounts to a doubt whether in the end any Hypothetical 
Judgment can be true, and points us again to a further type 
of judgment in which such deficiencies may be made good. 

The relation of Ground is thus essentially reciprocal, and 
it is only because the ' grounds ' alleged in every-day life are 
burdened with irrelevant matter or confused with causation 
in time, that we consider the Hypothetical Judgment to be 
in its nature not reversible. The habit of thought is to pro- 
ceed by determining an undetermined datum ; and this habit 
is never wholly laid aside even in the Hypothetical Judg- 
ment which is theoretically its negation. But a given condi- ^ 
tion, though interpreted in a single aspect by the judgment 
which draws its consequence, may have other consequences 
just for the same reason for which its consequent may have 
other (alternative, not merely co-operative) conditions. The 
' other ' conditions arise through a variation of the irrele- 
vancy present in the given condition ; as, if a circle has been 
said to arise through cutting a sphere in a plane, this con- 
dition may be varied by altering the superfluous relation in 
which a plane figure bounded by a line equidistant from the 
centre can be regarded ; e. g. it may be taken as a section of 
a cone, or as an ellipse with equal axes. And just as each 
of these irrelevancies would present the antecedent of 
circular curvature in different garb, so the presence of an 
irrelevancy which is thus capable of variation involves all 
the independent consequences that follow from the irrelevant 
idea in this case that of a sphere-section which has been 
included in the condition. If we restrict ourselves to the 
relation of equidistance in a plane, we can get no result 
beyond that of a circular figure with the properties which 
belong to it in the geometrical system. 

A ground that admits of such variation is not only partial 
or abstract, i.e. one which leaves the true ground in a measure 
to be understood, but is actually in part ' impure,' i. e. burdened 


Universal Judgment, 

[Book I. 

The idea 
of cause. 

Cause as 

with matter which gives rise to diverging consequences, and 
makes the ground itself one among many converging grounds. 

We have thus seen the idea of Ground in three aspects ; 
as an actual system, interpreted in its bearing upon its parts ; 
as a ' pure case,' i. e. a factor within a system stated in 
terms precisely relevant to the system and entering into a 
nexus in virtue of that system ; and as an ' impure case,' 
i. e. a condition weighted with irrelevant matter and so 
failing to express the real nexus which is aimed at. The 
first of these three is necessarily categorical in import, and 
may perhaps be identified with Schopenhauer's 'Seyns- 
Grund,' or Ground of Being ; the two others are primarily 
hypothetical and only imply reality behind them, and 
correspond together to his Erkemitnissgrund, or Ground of 
Knowledge. It need hardly be remarked that the ground 
of Being is also the only genuine and complete ground of 
knowledge. In respect of reciprocal character they must 
be divided differently; the first two, the complete and the 
abstract ground, being necessarily reciprocal with their con- 
sequents, and the third being as obviously not so. 

b. Cause may correspond either to the complete form or 
to the incomplete forms of Ground. In the former sense it 
can scarcely be taken to differ from ground at all. In the 
latter sense it is a distinct species which is included in a 
common genus with the incomplete forms of Ground. 

(1) Cause 1 as corresponding in meaning to complete 
Ground would consist in the exhibition of some selected 
attribute or event the effect in the totality of systematic 
relations which constitute its necessity. And in such mean- 
ing it can scarcely be taken to differ from Ground, because 
the temporal succession, which seems the natural differentia 
of Causation, disappears in the reference of the effect to a 
positive and continuous system. Mere temporal relation 
is negative, is nothing. It is only the unity behind the 
temporal relation that can bind cause to its effect ; and in 

1 Oa the conception of Cause, see some very acute remarks of Professor 
Clifford, Lectures and Essays, i. 150. 


Chap. vi.] Cause as 'Sum of Conditions! 265 

the real or complete Ground this unity is made explicit. 
The cause of the earth's being where it is at this moment 
may indeed be popularly indicated by saying that it was, 
wherever it was, at the previous moment ; but strictly 
of course the relation of the present position to the last 
position when fixed before the mind as discrete and succes- 
sive in time, is simply that the one is not the other, which 
is so far the same relation that subsists between the earth's 
present position and the sun's or moon's last position, and 
amounts to nothing at all. The cause of the earth's present 
position is the persistent velocity, together with the persistent 
influences regulating the direction, of its passage through 
space. This meaning of Cause is the ideal logical import 
of the term, and is what Mill meant to indicate when he 
defined C au s e as the { sum of the conditions.' T he word 
, ' s um ' is unfortunate, because it indicates a special way 
' which may be inappropriate of combining the factors. The 
totality of the relations would be a better phrase than the 
sum of the conditions. 

The only difference between Cause in this sense and 
Ground would be that Cause, though not a sensible 
event, still retains an import relative to the explanation 
of sensible events or of attributes entering into events 
(character, health, etc.), and is therefore not coextensive 
with Ground, which includes e. g. geometrical relations 
where the phenomena of process in time are wholly wanting. 
There would be no sense in saying that the attributes of a 
triangle are the cause of those of parallel straight lines, or 
vice versa 1 . The distinction, however, is more one of usage 
than of theory. On the one hand, the effect, subsequent in 
time, which is exhibited as one relation or difference within 
a necessary nexus, is necessary to the persistence of the 
whole system and to the evolution of its significance, so 
that the parts of the unity or system are reciprocally neces- 
sary in complete Cause as in complete Ground ; and on the 

1 Schopenhauer's ' Seynsgrund ' describes the relation of such cases, supposing 
the rational connection to be central and fundamental to the contents connected. 


Universal Judgment. 

[Book I. 

Cause as 
an event, 


other hand, if in investigating a ground, say in geometrical 
matter, we go back to the whole system of fact which is at 
the root of the necessary connection, we shall be justified 
in treating this fact as a Cause. We could hardly be 
censured for saying that the nature of space is not only the 
ground, but the cause, of the attributes of triangles and of 
parallels alike. 

Cause then, in its largest sense, is a real ground, and 
ultimately there is no complete ground which is not a real 
ground. Ground and Cause are thus not co-ordinate but 
convergent conceptions, i.e. as they are completed they 
tend to coincide, and the striking differences between them 
depend on a comparison of their imperfect and ultimately 
self-contradictory forms. 

Complete Cause, like complete Ground, corresponds to a 
Hypothetical Judgment whose condition and consequent 
are reciprocal. If, as is perhaps the case in Mill, the phrase 
' sum of the conditions ' is not limited to relevant con- 
ditions, and the hypothetical judgment which expresses the 
nexus of such a sum with its effect is consequently not 
reciprocal *, the notion of sum of conditions loses the only 
merit which it appeared to possess. But if it means, as it 
seems to mean, a persistent and systematic fact, then it 
agrees with other indications in suggesting that for the 
complete Ground or the complete Cause we must go 
beyond the Hypothetical Judgment. 

(2) Cause as an event in time is thus an imperfect 
conception. Indeed it is hardly possible to formulate the 
idea of one event in time as the cause of another that falls, 
in time, wholly outside the first. Cause is always taken to 
be more or less of a complication of relations and circum- 
stances ; and these, as acknowledged to bear on one 

1 Cp. Essays in Philosophical Criticism, p. 96 note. Of course if Cause as = 
sum of conditions is compatible with Mill's plurality of causes, the Cause as 
sum of conditions cannot = Ground. But it ought to be incompatible ; for in 
any concrete circumstance that may be named as condition, what is not relevant 
is not condition. So the sum of conditions ought to be restricted to the relevant 
or minimum conditions. 

chap, vi.] Cause as incomplete Ground, 267 

another, are not mere events in time. It may indeed be 
retorted that" mere time is an unreality and that no one 
ever said that causation was in mere time, i. e. in succession 
taken as discrete ; but that real time involves continuity as 
well as discreteness, and in such real time causation really 
is. Such a retort might be ill-founded as a statement of 
common logical opinion, but would in substance express 
the principle which I am endeavouring to explain. ; Mere 
time is mere succession ; but real time involves something 
that is not in succession, though it remains through suc- 
cession. The consciousness for which there is time has 
begun a process which tends to abolish time. To say that 
in this sense Causation is in real time is to say that Cause 
corresponds to an incomplete ground, i.e. a partially known 
unity including the factors which are in question as Cause 
and Effect. But when we come to speak of an incomplete 
Ground, the difference between thought and reality emerges, 
for it is only the complete Ground that is the real ground. 
When the ground in thought is distinguished from the 
ground in fact, then the cause is one with the ground in 
fact and is separable from the ground in thought, which 
latter is sometimes called by analogy the causa cognoscendi. 
Of course the causa essendi * must be a causa cognoscendi^ 
but a causa cognoscendi need not be a causa essendi. As a 
matter of fact the ground in thought or causa cognoscendi 
often belongs to the effect in time 2 , but may be any ele- 
ment whatever related to the real ground, whether cause, 
effect, or abstract principle. 

1 Schopenhauer's distinction between the Causa essendi (Seynsgrund) and the 
Causa fiendi (Ursache, cause proper) is reduced by the view taken in the text 
to a distinction of degree. Effect cannot be in succession to cause in the sense 
of falling outside it ; there must be a real whole which includes both. 

2 It is worth remarking as a matter of usage that ' antecedent ' in the con- 
ditional sentence has absolutely no allusion to the temporal relation of the 
events connected. Its name may have come from the usual grammatical place 
of the condition, or from some profounder idea of priority. But this would be 
a mere historical connection. Mill's application of the term to succession in 
time creates quite an unfounded idea of correspondence between Causation and 
the Hypothetical Judgment. 

268 Universal Judgment. [booki. 

The root of these distinctions is that the nexus of ground 
and consequence is at this stage still charged with irre- 
levancy. The cause a n d effect, gr ound and conseque nt, are 
all of them at this stage concrete events, or groups of incom- 
plete relations, among which the special aspects belonging 
to any nexus that may be in question have not yet been freed 
by analysis. As a result of this state of things the hypo- 
thetical judgment which embodies such a connection follows 
the analogy of singular judgments or of imperfect uni- 
versal, and has an antecedent which is not affirmed by 
affirming the consequent, just as the subject of a singular or 
generic judgment is not affirmed by affirming its predica- 
tion. And in so far as the hypothetical judgment is taken 
to be the natural vehicle in which to assert causation, this 
characteristic of it agrees with the popular vie w that th e 
s ame cause always has the same effert 3 h u t the same e ffect 
need n ot_al ways be due to the same cause . This doctrine , 
formujateoL_by MjlLjonder the nam eof^hg_phjral ity of 
causeSj.a.nd wholly ' incompatib le_ with his view wh ich treats 
Causeji s ' the sum of the conditions / is a mere translation 
into analytic science of the notion of subject and attribute, 
here quite out of place. The degree of truth which the 
view possesses depends solely on an imperfection of know- 
ledge and not in any way on the nature of causation. 

It is an old story that if, having said that 'All men are 
mortal,' you then further say that 'A. B. is a man,' you are 
committed to the assertion that he is also mortal ; but if 
you prefer to make the more cautious assertion that he is 
mortal, you do not thereby pledge yourself that he is a 
man. The same maxim in relation to the Hypothetical 
Judgment is summarised in the formula ' Assert the ante- 
cedent or deny the consequent.' It makes no sort of 
difference in the application of this formula whether cause 
is antecedent and effect consequent or vice versa. 

Thus the reason why the law of Causation has been 
stated in the form ' The same cause always has the same 
effect ' rather than in the complementary form ' The same 

chap. vi.] Same Effect, same Cause? 269 

effect always has the same cause ' is that popular philosophy- 
tends to start from the event which comes first in time, as 
logical antecedent, because the primary source of knowledge 
is simply to observe processes in time : and so the further 
determination of any datum or circumstance when effected 
by this elementary method corresponds to the succession of 
events in time, and that event which comes first is taken as 
the datum to be further^^ermined, and that which comes 
after is regarded as its deternjinatLon. Of course then the 
same datum always has the same determination, for every 
content and a datum is a content is an identity, and 
having attended to an identity in respect of one of its 
differences we are quite safe in saying that this identity 
this datum will always have the same difference. For 
if it seems not to have, we may say either that the difference 
is disguised, or that the datum is not the same. And so 
we come first to the principle that the same cause always 
has the same effect ; and sometimes, to make quite clear 
that we are simply regarding a real content in respect of a 
difference which we have selected out of its concrete nature, 
we add ' the same cause under the same conditions,' or * in 
the same relation;' thereby showing that we know very 
well that the concrete cause has all sorts of different effects 
under different conditions and in different relations. 

It is usually presupposing the truth of the first principle 
that we go on to consider whether the same effect always 
has the same cause ; and neglecting in the effect, which we 
take at first as a goal in which thought can rest, the idea of 
a limiting reference to a particular antecedent, we are im- 
pressed by the variety of relations and conditions compatible 
with the undetermined result, as contrasted with the single 
aspect in which we watch the operation of a cause ; and we 
forget that each set of these generates the effect in a slightly 
different form. It seems so common-sense to say ' If a man 
is drowned he is dead, but if he is dead he need not therefore 
have been drowned,' that we forget that, if he is dead in the 
particular way produced by drownings then he has been 

270 Universal Judgment. [booki. 

drowned. We might, from the very first consideration of an 
effect, draw a parallel to the popular form of the Law of Cau- 
sation, ' Same cause in same relation, same effect,' by a Law 
of Effect which should affirm, * Same effect, in same form, 
same cause.' But, as our first impression in starting from 
Cause is of the Identity of Effects, so our first impression in 
starting from Effect, because there is no simple guide to fur- 
ther determination, is of the Plurality of Causes. Really 
however we have to supplement these ideas by those of the 
Plurality of Effects and of the Identity of Causes. It is, tech- 
nically speaking, an accident which of these four points of view 
attracts our attention first. The knowledge that the. same 
effect has the same Cause is not necessarily later than or de- 
pendent on that of the converse maxim. 'Jf a man i s dead his 
heart has stopped \ doe s not involve a knowledge whether 
stoppage of the heart must always cause death. Still, as 
we saw, the common law of Causation is most readily sug- 
gested by our experience of simple observation, and has a 
certain real pre-eminence because of this experience. ^Ex.- 
pejtjmentall y we only follow up Causej nto Effect T n ot Effect 
into Cause. And thus the natural tendency is to identify 
Cause with Antecedent, and the common law of Causation 
' Same cause has same effect ' is the resulting one-sided 
application to Cause and Effect of the commonplace rules 
of the Hypothetical Judgment. Of course, when we have 
both principles together we have more than either alone ; 
but in itself neither prima facie involves the other. 

We have seen, then, that even the incomplete or partially 
known Cause can always enter into a Hypothetical Judg- 
ment either as Ground or as Consequent. In the same 
way it is possible for Effect to be either Ground or Conse- 
quent in Hypothetical Judgment. But Effect can never be 
Cause, unless we go back to the doctrine of complete 
Ground in which the boundary between Cause and Effect 
really melts away. Effect can never be Cause, and yet 
Effect may be as inevitable, as essential to the sequence, as 
necessary a Ground of hypothetical nexus as ever Cause 

chap. vi.] Why is Effect not Cause? 271 

could be. It is a well-known saying that we cannot con- 
ceive a storm to have been less violent than it actually was 
without the difference involving differences in a series of 
physical processes going back ad infinitum in the causal 
nexus. Yet we cannot bring ourselves to treat the storm 
as the cause of the previous physical processes which, as we 
say, resulted in it. The distinction which is at the root of our 
inability to do so is of course the distinction of Time. The 
operation of this distinction has never been more trenchantly 
stated than by Aristotle 1 , who lays down the general 
doctrine of Ground with perfect clearness, but in going on 
to deal with causation in succession doubts the security of 
all arguments from cause to a subsequent effect. For ' in 
the moment between the two, it would be false to say that 
the second has taken place, although the first has already 
taken place.' It may of course be rejoined that the cause 
cannot have completely taken place if the effect has not 
begun. This rejoinder however depends on the postulated 
unity of the causal process and on the consequent con- 
tinuity of time. If we press this point of view, it takes us 
back to the doctrine of complete ground, which consists in 
exhibiting the unity or continuity of causation regardless 
of succession in time. But we are anxious at this moment 
to do all we can in the way of elucidating the problem 
involved in the natural conception of causation as sequence, 
and therefore we will not simply fall back on this notion of 
complete ground. Granted that time and sequence are 
continuous, yet they are also discrete. There is indeed no 
empty fieragv or interval in which we can stand and say, 
' The cause is past and the effect is not begun.' But un- 
questionably we can make a stand at any point in the 
continuous sequence and say, So much is (or ' has been ') 
real, the rest is not yet real.' And what is not yet real 
cannot be the cause of what is or has been real. 

This appears to be the root of our whole conviction about 
cause and effect in time. Even after the entire sequence has 

1 Anal. Post. ii. 95 a, 30 ff. 

272 Universal Jtcdgment. [booki. 

been realised, and when all of it is alike real or unreal, as we 
may choose to count the past, still the objective temporal 
order into which we project our experiences embodies the suc- 
cession of relative reality and non-reality which attached to 
the order in its original constitution. We remember that 
this became real while that was still unrealised, and we 
therefore feel that however certainly they may reveal 
themselves as parts of a single whole, we can' never hold the 
event which came after to be an element in the actual 
determination of that which went before. It would involve 
to our minds the absurdity of treating the existent as caused 
by the non-existent. 

I do not mean to deny the reality of this distinction. It 
amounts to just what it is. Time is a condition, is the 
condition, is we may almost say the inmost nature, of our 
sensitive experience. The first operation of our intellectual 
synthesis is to build up an ideal objective order which, 
though itself not in time, yet contrasts as a more or less 
completed reality with the sensitive experience which is 
always passing into it. It is obvious that we can only con- 
struct our anticipation of reality out of its positive content 
so far as known to us ; and its positive content so far as 
known to us belongs to the past. We may fill up gaps in 
the past out of other parts of itself, but we can get nothing 
out of nothing, and therefore can draw no anticipations 
from the future. Therefore at any given moment we have 
no choice but to say that the future is conditioned by the 
past, and the past not by the future ; effect by cause, and 
cause not by effect. Cause, at any such given moment, is 
what we have, and effect what we have not. And further, 
taking the past as a representation of all that is, for it is the 
only positive content that we have to represent anything, 
we are right in saying that the past as a whole is the cause 
of the future as a whole. What is, is, and will act as it 
will act ; and what we already know of it is the only source 
from which we can anticipate its action. But of course the 
past as a mere series of events is past ; it has ceased to be 

chap, vi.] Reality of Succession. 273 

real just as truly as the future is not yet real ; the relation 
between two nothings is nothing, and cannot cause any- 
thing. The same applies to particular events; it is hard 
to find words which describe the negative relation of effect 
to cause, and which do not apply equally to that of cause 
to effect. Effect cannot be the cause of its cause, for the 
reason that it is absurd to find the cause of something 
existent in what does not (yet) exist. But is it less absurd 
to find the cause of what is now entering upon existence in 
what does not (any longer) exist ? Yet this is what we do 
if we take cause as an event and effect as a subsequent 
event. Hence we are driven to the second operation of our 
intellectual synthesis, which is, after erecting an objective 
temporal order not itself in time, to strip this temporal 
order of the importance attaching to its successiveness, and 
to treat it more and more as the expression of a plan or 
unity. Except as the expression of such a unity, causation, ^ 
as we have seen, disappears ; but as the expression of such 
a unity, the causal relation ceases to be in time, because the 
positive connection between cause and effect being made 
manifest, the two are united in the complete ground. This 
must be carefully distinguished from saying that time 
may be introduced anyhow without making a difference ; it 
does not mean that eggs boil water, or that death produces 
a revolver-shot. It simply means that the order of succes- 
sion, which has a largely negative aspect, disappears in the 
significance of a positive systematic connection, and that 
we do not in fact, in considering a past sequence, regard 
what came later in time as less fundamental or elucidatory 
than what came before. 

Then is not Time real? I answer that everything is 
real, so long as we do not take it for what it is not. 
Time is real as a condition of the experience of sensi- 
tive subjects, but it is not a form which profoundly 
exhibits the unity of things. And when we transfer 
the true judgment ' What has not yet happened must 
be a manifestation of the same unity which is involved 

VOL. I. T 

2 74 Universal Jtidgnient. , [Book i; 

in what I already positively know' to a totality which is 
already in all its parts equally real, we confuse, and give 
' time ' a reality which it has not. Such a confusion is 
involved in the idea that there can be no more in the effect 
than there was in the temporal cause, and in the tremendous 
power consequently exercised by historical analysis over 
common minds. The confusion is reinforced by another 
aspect of causation. Practice, like sensitive experience, is 
in time. In translating a plan into practice, the relations 
of succession hold good. A sequence is what it is, and 
nothing else ; and a reversed sequence would simply be 
different. Therefore for practice the earlier event is more 
important, in the sense in which the means is more im- 
portant than the end. For knowledge of the end does not 
give power to produce, but knowledge of the means does. 
But this importance begins and ends with practice, and 
even there it only exists in virtue of the unity whose nature 
is expressed for us in the fabric of ideal reality a fabric 
which is not in time. 

Thus it is easy to see the relation between Cause and 
Ground in the imperfect stage in which they are dis- 
tinguishable conceptions. Ground is a content which is 
perceived, by reason of any systematic relation whatever, 
to involve the determination of another content. Cause is 
also a Content perceived to involve the determination of 
another content, and is therefore a kind of Ground, but is 
primarily confined to the special case in which the deter- 
mining content is real and the determined content unreal. 
But as this is merely a negative relation, even the first pre- 
sumption of causation in some degree supplements it by the 
postulate of a positive nexus, and we know very well that 
in practice if no positive nexus, no continued identity of 
process, can be alleged, we do not allege causation. A 
familiar illustration is the sequence of day and night. It 
is generally urged that if causation were mere succession, 
day must be the cause of night, but that really day is not 
the cause of night, because both are effects of a commoi 

chap. vi.] Night and Day. 275 

cause, and either might very well go on without the other. 
This is one of those trivial examples that seem hardly- 
worth arguing about, and yet, if argued about, must be 
treated at length. I have shown that I at least think 
* Causation = mere constant succession' plainly false andf 
in contradiction with facts; but if I must discuss this easel ft . . 1 

I should like to have the terms defined. The question, as I f y<^\ * 1 
take it, is, Does 'day' in the sense in which it is here used i 
include a unity, a system, a principle, which is continuous J 
in and responsible for night ? If so, day is the cause of " 
night ; if not, not. The reason why we think it wrong to 
call day the cause of night is not because night has the 
same claim to be called the cause of day. There is no 
contradiction here. In our ordinary way of treating imper- 
fect causation there is no reason why the daylight hours of 
Monday should not be the cause of Monday night, Monday 
night of Tuesday, Tuesday of Tuesday night, and so on. 
The difficulty does not lie in the sequence being of this 
alternate nature a single oscillation of a pendulum is cer- 
tainly the cause, though not the complete ground, of the 
next but that the persistent unity which lies at the root of 
both phenomena does not fall within the natural definition of 
either. If day meant not merely the presence of light on 
the earth's surface, but, in relation to any given point on 
the earth's surface, that portion of the earth's rotation 
which carried that point from its sunrise to its sunset, then 
I do not see how it could be denied that this portion of 
rotation, in as far as it determined the position of the 
selected point throughout the immediately succeeding sec- 
tion of the rotation, was the cause or principal condition of 
the ensuing night. But of course the name 'day' is 
applied e. g. to the six months' day of the poles only by 
metaphor, being a chronological idea which has become 
largely independent of the relation of a particular place to 
the sun's illumination, and having legal and social meanings 
which do not admit of an antithesis with night. So the 
true reason why we do not like to predicate causation of 


276 Universal Judgment. [booki. 

this sequence is simply that, owing to their varied accessory 
significations, the terms day and night do not apply to suc- 
cessive stages of a continuous natural process, but are mere 
chance distinctions that are drawn, according to our shifting 
purposes, on the surface of that process. 

But though we do not allege causation where we cannot 
allege a positive nexus, yet, as I pointed out above, there is 
a considerable distinction of degree between the objective 
temporal order and the intelligible unity of things. The 
less we advance beyond the stage of perception and narra- 
tive to that of science and intelligence, the more does the 
negative distinction of time retain its significance. Strictly 
speaking, the distinction between cause and effect in time is 
only real at an arbitrary moment in which we draw an 
ideal, line across the temporal process of sensitive experi- 
ence, between the real and the unreal. When cause and 
effect are both absorbed in the past, the distinction is only 
transferred by memory into the content of reality, which thus 
takes the form of the objective temporal order. This order 
would be an intolerable chaos but for a certain presumption 
of causation, i. e. of unity, which binds it together according 
to some sort of system ; there is no real history apart from 
the idea of causation. Nevertheless this unity remains for 
the most part inchoate, i. e. only in some degree explicit ; 
and so, though not itself in time, presents the scheme of a 
de facto evolution in time as a sort of extended memory, with 
the transferred character of determination of unreal by real, 
i. e. of effect by cause. Now it is plain from what has been 
said that the distinction of Cause and Effect is self-destructive. 
It is utterly impossible to be successful in the investiga- 
tion of a causal relation without reducing it to the intelli- 
gible unity of a complete ground. History therefore, in 
the sense of the mere record of remembered fact, would seem 
to have for its ideal to disappear into systems of hypo- 
thetical judgment, in which complete ground should do 
duty for cause and effect, and the relation of time should 

chap. vi.] Histoiy and Science. 277 

This conclusion is true, in my judgment, in relation to 
the mere phenomena of the past, and the resulting con- 
nection between causation and ground. But as regards 
what we really mean by history, such a conclusion is repug- 
nant to our feelings and inconceivable to our understanding. 
The reason is plain. History is not merely a name for the 
recorded past. A series of astronomical observations is 
not history; it is science, and has no value but for 
science, unless by chance it throws light on the observer's 
character or on the state of science in his time as an 
element in the condition of man. What we mean by His- 
tory is the revelation of man's nature in action and intellw 
gence. And when we deprecate the reduction of history to 
a system of hypothetical judgments founded in some single 
abstract individuality to a science like abstract mechanics 
or abstract economics what we really mean is that man's 
nature reveals itself in individuals, in actions, in forms of 
intelligence, and we do not want to lose these realities in 
abstractions of relativity and necessity. But if we consider 
that hypothetical necessary or relative judgment is entirely 
based upon categorical judgments, that all nexus is within 
an individuality, we shall see that history may be received 
into the intelligible unity of knowledge without sacrificing 
its concrete import and characteristic significance. This 
could only be destroyed if we insisted on predetermining 
within what whole or system we should find the facts of 
history to be necessarily related. 

And no doubt a suspicion of some such prejudice is opera- 
tive in the reluctance to absorb history in ' science ' to which 
I have adverted. If science meant exclusively the sciences 
which grow out of the one-sided forms of measurement, 
then we should rightly deny that there is a science of history, 
and, for the same reasons, that there is a science of art, of 
political form, or of religion. We escape however from such 
suspicions if we remember that all connection is based on 
fact, and all analysis on individuality; and that the nature 
of the facts or of the individual whole or system with which 

27B Universal Judgment. [booki. 

a science deals can ex hypothesi be only for that science 
itself to determine. 

Thus the conception of Cause as an event in time anterior 
to effect gives way on analysis, and forces us back to the 
conception of the complete Ground ; and the conception of 
incomplete Ground (causa cognoscendi)^.^ distinct from Cause, 
expands into the same unity, which, as we saw, is at once 
the complete Cause and the real Ground ; i. e. the relation of 
part to part within an actual and systematic totality. This 
relation of part to part, either burdened with irrelevancy as 
in the ordinary hypothetical judgment, or pure and relevant 
as in the hypothetical judgment whose terms are reciprocal, 
forms the content of the abstract universal judgment. And 
this abstract judgment is a divergence from the concrete 
evolution of thought, and joins with the mediate and quasi- 
generic* judgments of the sciences which arise out of one- 
sided measurement l . But it may also be regarded as an 
element in or aspect of the popular or transitional quasi- 
collective and the generic judgments which are enumerative 
or individual in form but analogical in meaning. Analogy, 
as we pointed out, is compatible with systematic necessary 
^ On the otlfier hand, though a complementary aspect of 

the universal judgment, the pure hypothetical is destitute 
of finality, and incapable of standing alone. It demands a 
reversion to concrete thought by the fact that it presupposes 
a self- existent whole. Apart from such reversion it may 
become a wholly arbitrary and meaningless play of fancy, 
presupposing conditions which are not made explicit. 

As I have not yet dealt with negation, I shall leave the 

negative forms of the hypothetical judgment to be dealt 

with in the same chapter as the disjunctive judgment, with 

which they are closely connected. 

Supposi- c. The above appears to me to be a fair account of the 

universal hypothetical or abstract universal judgment considered 

judgment. f r0 m a strictly logical point of view. In one important 

1 See Scheme, p. 92. 

chap, vi.] Idea as Stibject. 279 

respect however it is prima facie at variance with con- 
clusions which might be drawn from the grammatical 
shape of these predications as to the attitude of mind in 
which they are normally made. The point in doubt is the 
existential significance of the universal judgment. The 
account which I have given treats the existential implica- 
tion which attaches undoubtedly in very various degrees 
to the different forms of the universal judgment, as cog- 
nate with the existential affirmation involved in the singular 
and in the perceptive judgments. But it has been trench- 
antly laid down by Mr. Bradley that a different view is 
suggested by the attitude of the mind in all purely abstract 
judging abstract be it remembered not necessarily in 
content, but only as all thought is abstract when contrasted 
with sense-perception. I am unable to reconcile this view v 
with the existential value of judgments about individuals 
designated by proper names, in which there is no direct 
reference to sense-perception nor to anything but a content, 
whose real existence is as I imagine taken to be asserted 
owing to its concrete nature. But I proceed at once to 
discuss the analysis of the abstract universal affirmation, 
from the point of view to which I allude. 

It will be remembered that in the general discussion of 
the nature of judgment, we agreed that the ultimate subject 
in judgment was never an idea, never that is to say even 
a logical idea or content, for the particular psychical image 
we found not to concern us in logic. The ultimate subject 
in judging was always, we held, the Real, which in the act 
of judgment is qualified by certain logical ideas. So long 
as the immediate subject was present perception, whether 
additionally qualified by designative ideas or not, all went 
smoothly, for the immediate subject was then simply the 
point of contact with the ultimate subject of judgment. Some 
difficulty, indeed, arose in explaining the real reference of the 
Singular judgment in which the subject may fall outside 
present perception and may have to be united therewith by 
a constructive process. Still, however, the immediate sub- 

280 Universal Judgment. [book i. 

ject was a determinate element in the whole of Reality, 
having individual existence manifested within the sensible 
series, although e.g. in the case of an organism, still more in 
the case of a man, not of a kind that could really be pre- 
sented by sense-perception as such. So far therefore we 
were, in judging, referring an ideal content to reality in 
some particular concrete aspect, and therefore our Judgment 
was still plainly existential, i.e. such as to become false if 
the concrete element of reality described had no place in 
the series of sensible events. 

Now when we come to deal with the Universal Judgment 
it must be admitted that at least as a question of form the 
reference to reality becomes less easy to define. The 
pseudo-collective and the analogical judgment at any rate 
(dismissing the conception of the individual generic judg- 
ment, in which the singular judgment revives) are unques- 
tionably capable of an interpretation which reduces them to 
the pure Hypothetical Judgment. In our old acquaintance 
'All men are mortal' the ' all' is too obviously not collective 
to stand in the way for a moment. We certainly might be 
driven to confess that in so judging we had only asserted 
' If man, then mortal ' or ' Where man, there mortal.' Such 
an interpretation is involved no less in Mill's analysis of the 
import of propositions than in Lotze's or Bradley's treat- 
ment of the universal judgment. To affirm co-existence of 
attributes is not to affirm existence of subj ects l . The analogical 
judgment has this aspect even more plainly. 'An organism 
as such is mortal' means, it may be urged, if taken strictly 
and without counting implications, w If organism, then 
mortal,' ' Where organism, there mortal,' * Whatever is 
organic is mortal.' If in consequence of such an assertion 
we take it that organisms are actual elements of the real 
world, this is implication though very strong implication 
and not assertion. 

1 This comes out very emphatically in Mill's account of Definition, which 
when Real at all, he analyses into a meaning and a postulate of existence. In 
this he is pretty much at one with Mr. Bradley's account of universal judgment. 
See also Mill's account of mathematical truth. 

chap, vi.] The nature of Supposition. 281 

According to this analysis, the essence of which is to 
regard the implication of existence in these judgments as 
outside the matter affirmed, all abstract affirmation abstract 
merely in the sense of not referring to present perception or 
to particular sensible events is on the level of hypothesis, 
has for its immediate subject an idea not a reality, and 
consequently has no existential import, or ' deals purely 
with adjectivals 1 .' 

The identification of the universal judgment as such with 
affirmation based on hypothesis being thus made, the further 
development of the view turns on the nature of hypothesis v r 
or supposition. The essence of supposition is that it is qua 
supposition, wholly arbitrary in its starting-point. Its con- 
tent is taken, not given, is an idea, not a fact ({{per accidens 
a fact, is not used as a fact, i. e. its existence is not argued 
from), and is considered not in itself, but for the sake of its 
relativity, i. e. for what flows from it, for its consequences. 
The essence of supposition is in short argument from content, 
and not from existence of content. The consideration of 
any proposed legislation, e. g. a Reform or Land Act, with 
reference to its consequences, is an example of supposition. 
' Suppose every adult male to have a vote, it will be impos- 
sible to maintain indirect taxation;' 'Suppose Ireland to have 
a Statutory Parliament, the Imperial Parliament will by this 
fact itself become statutory/ Or again, ' Suppose beings 
endowed with perception but confined to a plane in the ex- 
ercise of it, they must see all figures as lines or points.' 

The process is to select or to fabricate, apparently at 
pleasure, an ideal content, to think of it as in connection 
with some known reality, and to judge the result as a truth 
conditional on such connection. 

It is plain that in this operation, subject to a certain 
reservation to be mentioned directly, the supposition selec- 
tion or fabrication 2 of content is arbitrary, but the judgment 
proper is necessary. 

1 Bradley's Principles of Logic, p. 81. 

2 Selection and fabrication differ only in degree, not merely because all 

282 Universal Judgment, [booki. 

What then, precisely, it has further been asked, is in 
such a case affirmed about ultimate Reality? Plainly, not 
the existence of the content as a fact in the context of our 
world. We may take Sigwart's instance, reproduced by 
Bradley. ' Si tacuisses, philosophus mansisses.' Something 
is here affirmed, but not the actuality of the content, which 
is by the strongest implication denied. Or again, 'All tres- 
passers will be prosecuted.' The truth of this declaration 
does not depend on there being trespassers, though it cannot 
be tested unless there are trespassers. 

When we have once accepted this point of view, and 
excluded as unessential the various implications of existence 
which attach to various Universal Judgments, the conclusion 
is inevitable. Judgments so regarded do not affirm as true 
of Reality any explicit content or even any connection of 
explicit content. We have seen that it is no impeachment 
of the judgment that its content never has been nor can be 
actual. ' The necessary may be impossible or non-existent V 
And as for the connection of content, though it is necessary, 
yet it cannot be actual unless the content to be connected is 
actual, and the judgment may be true though the content 
be incapable of actuality. Therefore the truth of the judg- 
ment, according to this extreme analysis, depends neither 
on the actuality of its content, nor on the actuality of the 
connection it alleges within its content. What then does such 
a judgment assert of that Real which is the ultimate subject 
in every judgment ? Simply this, that the Real is such that 
under the ideal condition which forms the immediate subject 
of the judgment it will furnish the ideal consequent which is 
expressed in its predication. The hypothetical judgment 
would then be illustrative but not enunciative of Reality. 
The property of Reality which it illustrates may however 
be accessible to knowledge ; or again, according to the view 
before us, it may not. Simple examples of the former case 

fabrication is selection, but also because all selection is fabrication involves 
the constitution of an idea from a given or chosen point of view. 
1 Bradley's Principles of Logic, p. 186. 

chap, vi.] Idea of Supposition criticised. 


form the best explanation of the conception which we are 
discussing. ' If you ask him for money he will refuse you.' 
The real quality of the real man, on which this prediction 
rests, may be that he is a miser ; then his miserliness x is 
the real fact, not apparent in the judgment, which the sup- 
position and consequent a and b only illustrate by its effect 
in an ideal case ; and which is categorically affirmed, but 
only as an unknown x, in the Judgment. And it is conceiv- 
able that the property of Reality which lies at the root of 
the judgment may not be known, and wherever the connec- 
tion envisaged as hypothetical is considered to be ultimate 
and not susceptible of further explanation, the property of 
Reality at its root is pro tanto unknown. Such a connec- 
tion would be, I suppose, ' Whatever is material, has gravity.' 
The property ;tr of reality which is here categorically asserted 
as the basis of this connection, ' If a then b,' is, I presume, 
and is likely to remain, unknown. 

The real criticism which I have to offer upon this view 
is contained in the whole account of judgment which has 
been submitted to the reader. Its point and purpose have 
been to exhibit the aspects of fact, and of relativity or 
necessity, within the judging function as complementary 
and inseparable, but as differently predominant in dealing ; 
with different contents. Consequently, the abstractness 
on which their respective predominance has hinged, has 
been treated as the abstractness of contents, and not as 
that formal abstractness which is merely the mark of 
thought as opposed to sensuous perception. And the 
result has been to exhibit the graduated existential im- 
plication of universal judgment as falling within and not 
without the import of those judgments, and as homologous 
with the aspect of existential affirmation in perception 
and in historical narrative. But I propose to comment 
very briefly on two special problems raised by the view 
before us. 

(1) It is easy for any one to form for himself a catena of Simple and 
universal judgments, beginning where the proper name judgments. 


284 Universal Judgment. [booki. 

becomes significant, as with Europeans, Christians, Peelites, 
and passing on through the generic conceptions of classi- 
ficatory sciences, to physical and mechanical principles, 
geometrical axioms or theorems, and finally to imaginary 
and impossible but self-coherent hypotheses, like that em- 
bodied in the ingenious jeu d esprit entitled ' Flatland.' 
Such a catena is at the root of the view of Universal 
Judgment which I have endeavoured to formulate. Any 
one who will take the trouble to follow up and to fill 
out with instances familiar to himself the terms of such 
a series, will hardly be able, I think, to avoid forming the 
conviction that no single type of proposition is adequate 
in the same degree to the content of all universal affir- 
mations. If, however, we are compelled to choose, the 
conditional proposition is the more adequate. But it 
is not adequate. Such a judgment as 'All Christians 
hold that God is a Spirit ' combines collective and generic 
meaning with necessity. It indicates not merely that the 
doctrine is of the essence of Christianity, i. e. that ' If 
a man is a Christian he holds ' etc., but that there is 
a Christian world, realised in many individuals, which is 
united in this conviction. 

And on the other hand, after our too laborious con- 
sideration of the subject, it is not necessary to remind 
the reader that relativity is operative within the judgment 
from the moment of the first analysis introduced by 
perception into the data of sense ; that is to say, even 
when the judgment assumes the external form of the 
impersonal proposition, which indicates that identifiable 
subjects are not yet constituted in virtue of determinate 

The fact then is this. Speech can express no logical 
relation except by making it the correlative of a word 
or clause. But the common types of speech, which have 
been made the basis of logical investigation, are direct and 
simple. They therefore embody only one aspect of the 
concrete logical thought, and leave all others to be guessed 

chap. vi.] Self-defence of the Hypothetical. 285 

at from variety of context and the requirements of content. 
The process of recognising explicit linguistic correlatives 
of relations which in these direct forms are only implicit is 
a slow process Aristotle did not recognise the conditional 
proposition on its merits and begins, as is usual in such 
cases, by substituting one-sided abstraction for unanalysed 
confusion. Therefore by adopting either the direct or the 
conditional mode of expression we ignore in the first 
case, and formally exclude in the second, elements without 
which it is impossible for judgment to exist. The direct 
or ' categorical ' form is used till it breaks down under the 
burden of an import for which it was not invented ; and 
the conditional form then takes its place, to express the 
relative import, the determinate and restricted reference 
from part to part within a whole, which now insists on 
making itself predominant. But both forms, not one only, 
are inadequate to their content. The content of categorical 
assertion has relativity, and that of hypothetical assertion 
has absoluteness. But categorical assertion (I am speaking 
of grammatical form) leaves the former, and hypothetical 
assertion leaves the latter to be implied. The two forms 
however have not an equal right to the ground they 
commonly claim. The first comer has, naturally, occupied 
all it could get, and more than it could adequately deal 
with. It is against this encroachment of the categorical 
judgment-form that modern logicians have rightly espoused 
the cause of the hypothetical. The true frontier is, beyond 
a doubt, where the singular judgment ends. After that 
point, if we dismiss the Individual Universal and omit 
to consider the Disjunctive, the purpose of assertion is 
relativity or sequence, and absoluteness or existence is only 
its presupposition. Formal Logic granted this territory, 
that of the pseudo-collective and the analogical judgment, 
to the Categorical Judgment, simply because it found the 
Categorical or direct Proposition in possession. 

And the further analysis of the irrelevant connections 
which encumber every perceptive and singular judgment, 

286 Universal Judgment. [Booki. 

and which, if understood to be generally affirmed, imme- 
diately become false, may be regarded as a reprisal on 
behalf of the hypothetical judgment, which, now that 
attention has been drawn to the meaning made explicit 
in the conditional sentence, threatens to dislodge the 
categorical judgment even from the fields of perception 
and of history. The degree in which such a claim should 
be conceded has been indicated above. 

Thus the simple and the conditional 1 propositions are, the 
one of them an indeterminate and the other a one-sided 
type both therefore imperfect expressions of thought. 
The latter is borrowed no doubt from, or is at any rate 
most appropriate to, the extreme and arbitrary attitude of 
mind known as supposition. It is natural, as we have seen, 
that the empire of the first comer should not be broken 
into. unless a forcible demand arose for something utterly 
incompatible with its type. The representation which is 
correlative to supposition is thus the sole representation in 
ordinary speech of the aspect of necessary sequence within 
the judgment. This is why, when logic awakens to this 
aspect, it is tempted to find its essence in supposition. 

But supposition is not the essence. Supposition is 
intentional abstraction or selection culminating in fabri- 
cation ; and the essence of the judgment is not in the fact 
of intention, but in the logical ground and justification of 
the intention. The interference of the will is no differentia 
in a logical process. All thinking presupposes will, but 
the guide of thought can never be moral purpose, the 
purpose of will, but must always be logical necessity. 
What remains then out of the fact of supposition is that a 
content is taken, chosen, fabricated, if we will, with a view 
to its relative aspect, to its consequences. But what is 

1 The grammatical difference between the two is connected with their logical 
import in that the conditional sentence provides for an express analysis ad hoc 
of the subject-qualification of Reality, whereas the direct sentence simply indi- 
cates a subject-content by a name. If we insist on the name being the right 
subject name in the context, as in Aristotle's tca66\ov, we have an intermediate 

chap, vi.] Unknown basis of Hypothetical. 287 

presupposed in so taking it, and what are the conditions 
under which alone it can be so taken whether, that is, 
it can be taken in the air and without either self-relation 
or relation to an actual system, are questions in no way 
touched by the mind's attitude in supposition. We shall 
see that speech finds the embodiment of a necessity resting 
on fact in the proposition which expresses the disjunctive 

(%) The quality x of Reality on which the sequence ' if a The basis 
then b ' depends may be, and is in ultimate sequences so JheticaT" 
far as ultimate, unknown. This follows from the reduction Judgment. 
of the abstract or universal judgment to judgment based 
on supposition. But it follows from our analysis of the 
hypothetical judgment that if this were so, the back of the 
sequence would be broken. The ground would be absent. 
Every hypothetical judgment is affirmed only within an 
actual system. What then are we to do with our ultimate 
sequence, e. g. with the nexus between resistance and 
gravity? I cannot but maintain that, if we have no 
explicit ground to go upon, we must either surrender 
the sequence altogether, or affirm it categorically, i. e. 
not as a sequence, but as a datum ; not as a coherence, 
but as a conjunction. ; A11 matter (i.e. all that resists) 
gravitates' is no doubt a judgment in which we look 
for necessity. But it does not follow that we find it. 
It presupposes the judgment ' There is gravitating matter.' 
It is not adequately rendered by ' If or wherever there is 
matter it gravitates.' We are unable (or at least I am 
unable, which is all that my illustration requires) to assign 
any system which acts as ground and compels the sequence 
to be true within it. The world of matter given as 
resisting and gravitating, as a systematic fact, is the 
ground. And therefore it is on the other hand a true 
hypothetical judgment to say, ' If a material object is 
set free within range of a gravitating centre, it falls with 
a velocity accelerating as the squares of the times.' For 
the content of this judgment is within the system of 

288 Universal Judgment. [booki. 

gravitating bodies, and the sequence is compelled by that 
system, whose existence as a fact is required by the judg- 
ment, but not in this form explicitly asserted. In this case 
the unity of gravitating matter is the x on which the 
sequence a-b is founded. 

May not the whole system be supposed, ground and all ? 
Certainly not) and this is the fundamental point at stake. 
Every judgment is a qualification of reality by some ideal 
content, and when the basis of a sequence is the content by 
which reality is qualified, that basis is by the judgment 
affirmed to be actual. So far Mr. Bradley and I are 
together; my further contention is that this ground or 
basis must be known, and must be indicated in the judg- 
ment, of which it forms the essence. The degrees in 
which it is so indicated form the various complete and 
incomplete grounds which were discussed above. But an 
ultimate ground must be actual ; it is the fact which is 
judged in a hypothetical judgment. We may of course 
freely suppose or imagine a system, as complex as we 
please ; but if we proceed to judge about the consequences 
or results of such a system, it must thus be related to these 
consequences within some further system ; and this further 
system must be actual. In other words, you can only 
suppose an antecedent, you cannot suppose a consequent ; 
the consequent must be judged, not supposed; and in 
judging the consequent you assert the underlying ground 
to be actual. 

This may be illustrated by the extreme cases in which 
we refuse to entertain a supposition. This means that we 
are not aware of any reality which furnishes a system such 
that the supposed case is capable of entering into it. When 
supposition begins to infect the nature of the reality, we 
are beginning to suppose and not to judge our sequence. 
It is quite doubtful whether the conclusions of ' Flatland ' 
can be taken as true even qua hypothetical judgments. 
When your supposition has knocked the keystone out of 
actual reality, how is it to support a conclusion? 

chap, vi.] Illegitimate Suppositions, 289 

The application of this Conception would I think solve 
the curious cases in which a sequence is true, though it is 
possible for the content of supposition not to exist, or even 
impossible for it to exist. What must exist is a system 
that, subject to the supposition, necessitates the conse- 
quence drawn from the supposition. Whether the content 
itself exists or not depends upon whether it is an 
element essential to the system ; and how it exists, on 
the nature and self-completeness of the system. The 
former condition meets the case of impossible contents, 
which are in every case illegitimate suppositions i.e. sup- 
positions in which the consequent has to be supposed and not 
genuinely judged, because the supposed antecedent conflicts 
with the nature of the real system on the basis of which 
alone any conclusion about it can be drawn. 

I will take some examples. ' Given a first cause, we can 
dispense with the idea of a regress to infinity.' But Cause, in 
any sense which it could be First, i.e. in temporal relation, 
means an element in a system of relativity. Therefore the 
idea of a first cause contradicts the whole actual system to 
which the idea of Cause refers, and it is utterly impossible 
to affirm anything about an idea which begins by destroying 
its own basis of affirmation the causal system. Or again : 
* If one man were throughout the whole period of his 
conscious life alone in the universe, his moral purpose 
could be nothing but to please himself.' Here we are 
judging on the basis of an existing moral world for it 
is only this that gives a meaning to a judgment relating 
to moral purpose but we are putting a case which con- 
tradicts the nature of man as a being existent in a moral 
world. I do not think that in this case any judgment can 
reasonably be made. But the purposes of supposition in 
argument are so various, for its object may be in different 
degrees to emphasise the impossibility of the content 
supposed, that the limits of legitimate supposal are ex- 
ceedingly hard to define. Undoubtedly its use is one of 
the most fallacious if one of the most effective means of 

VOL. I. U 

290 Universal Judgment. [booki. 

controversy. ' If A. B. were to turn coward ' ' But he 
could not' 'But I am only putting a case' 'But if you 
put such a case I may put any consequence I choose as 
equally likely,' i.e. it is felt that the real basis on which 
judgment rests is annihilated. 

This real basis can never be dispensed with in judgment. 
The nearest approach to dispensing with it is made when 
elements of reality which would conflict with the suggested 
case are wilfully kept out of account by an act of abstrac- 
tion ; which act of abstraction may be either borne in 
mind, or forgotten. If the act of abstraction is borne in 
mind, we obtain such judgments as those in which mathe- 
matical science deals with imaginary quantities 1 . Thus 
judgments are subject to the reservation implied in the 
abstraction from reality which enables them to be made. 
Yet, in as far as they are judged at all, they must rest upon, 
and involve the affirmation of, properties of reality. If the 
abstraction is forgotten, we then obtain such judgments as 
apply imaginary conceptions without reservation to the real 
world ; 'A conjuror can tie a knot in a string whose ends 
are held, because he understands the properties of four- 
dimensional space.' 

I may further illustrate this last case by the example 
of artistic fiction, which I have discussed at length else- 
where. It consists of judgments both singular and 
universal 2 , made on the basis of human nature, but subject 
to a reservation which separates them from the world of 

1 See p. 1 74 ff. on mathematical infinity. 

2 It may be doubted how far the universal judgments in a fiction ought to 
partake of the character of fiction. It depends on their grade of universality. 
Judgments of a reflective order, about human nature for instance, if not dramatic, 
are expected to be true without reserve. Judgments about parties, nations, etc. 
may be fictitious. Dramatic sayings are yet more complicated ; they are not 
judgments of the author at all ; the author's (fictitious) judgment is that they 
were uttered. Then their value or merit is compounded of their truth as 
estimated by the limited reality of the drama in which they occur (i. e. their 
appropriateness) and of their truth as estimated by real reality, i. e. their weight 
or depth, which of course involves the whole relation of the piece to real 
reality. Vid. Knowledge and Reality, p. 1406. 

Chap, vi.] Affirmation of Sensible Events. 291 

past sensible events. While actually under the spell of 
romance or of the drama, we forget or half forget this 
reservation ; but we do not and cannot forget the true 
and ultimate basis of the judgments, fundamental human 
nature, which is the ground and substance of the whole 

But we raised a question not only whether the content 
exists, but how the content exists. This depends, we said, 
on the nature and self-completeness of the system within 
which it exists. Many universal judgments deal with 
sensible events, which are not, within our knowledge, 
contained in any really concrete whole in time and space. 
For these, according to the principle which we have 
followed throughout, the abstract universal or hypothetical 
judgment postulates such existence as they can have, 
according to their nature and that of the incomplete 
system to which they belong. There is nothing which 
cannot ultimately be taken up into some individuality 
by constructive thought. But as in ordinary judgment 
no such actual construction is operative, we have to 
substitute for it the mere assertion of the basis to which 
the sensible occurrence in question is known to have some 
relation. The imperfect explicitness of this relation is the 
note of distinction between the hypothetical and the 
disjunctive judgment. 'Pure red is ethereal undulation 
impinging on a normal eye with x vibrations to the second.' 
Here the ground or basis of affirmation is the existence 
of light, which is ultimately dependent on the existence of 
sentient organisms in a certain relation to the material 
world. Now this relation, though not known nor explicit 
in the judgment, must be taken as knowable and real. 
Space and Time indeed produce the illusion of endlessness ; 
but no special positive content like sentience or light is 
involved in this illusion ; we rather assume every positive 
content to have its own time, place and conditions within 
our actual individual system. No doubt we may be asked, 
Does the above hypothetical judgment assert the existence 

U 3 

292 Universal Judgment. 

of red, or not ? And can we claim to assert the reality of 
what is for us an indeterminate endless series which as 
a whole cannot be real? To these questions I should 
propose to reply: 'The hypothetical judgment in question 
asserts the existence of light as the categorical basis of the 
nexus which it selects. The existence of red light is 
involved in the existence of normal light-stimuli and normal 
eyes. Therefore the judgment in question asserts the 
existence of red light as a feature of the reality constructed 
by and for us, and subject to the reservations which its 
position in that reality imposes on it. We do not claim 
to assert the reality of an endless series of sensations as 
such ; but in the first place a positive series as referred to 
an actual system is already placed beyond theoretical end- 
lessness, and in the second place it is not as an occurrence 
in the way of sensation that we assert its reality, but as 
an attribute of things in the whole of consciousness, which, 
as constructed out of perception, is for us the only reality.' 
This is in effect the answer which was given above to the 
question whether the conceptions of geometry were judged 
to be real ; and it follows inevitably from the considerations 
to which we were led in treating of the doctrine of Ground. 
We shall see that the real Ground, when made explicit, 
takes us into the province of the disjunctive judgment. 
The element of categorical assertion in the hypothetical 
judgment, consisting as it does in some underlying real 
attribute, also presents a close analogy to the positive basis 
of negation, as will appear in the following chapter. 

Negation, Opposition, and Conversion. 

i. The Negative Judgment presents at first sight a para- Negation 
doxical aspect. We are bound to take it, qua judgment, firmatfon 
as playing some part in knowledge, and as at any rate 
capable of contributing some factor to the ideal fabric of 
reality. But it assumes the external shape of ignorance, or 
at least of failure, and the paradox consists in this that in 
negation the work of positive knowledge appears to be per- 
formed by ignorance. The contradiction arises, as we have 
seen other contradictions arise, from the adoption by 
thought of a shape which at best expresses it but partially, 
and the retention of that shape when the aspect which it 
did express has come to be dwarfed by other aspects of 
knowledge. But of course the shape could neither be 
adopted nor retained did it not in some prominent aspect 
coincide with the requirements even of developed thought. 
Here then, as elsewhere, the key to our problem must be 
looked for in the conception of the individual mind working 
out its participation in reality by help of forms never wholly 
alien to this aim, but profoundly transmuted in proportion 
as it is attained. 

Negation is at first sight merely negative. It appears to 
say nothing, but only to deny, i. e. to put away some ideal 
content as other than reality or to express our inability to 
recognise it as belonging to reality. The first step then 
towards ascertaining its import is to ask, what does it deny 
or pronounce unreal ? what does it presuppose to be pre- 
sent before denial is possible ? 

It certainly does not presuppose an affirmation. Both 
fact and theory protest against such a view. We have not 
always judged a matter to be true before we deny it. And 

294 Negation, Opposition, and Conversion, [booki. 

if an affirmation 1 of the same content is to subsist as a con- 
dition of the negation, it seems doubtful whether a negation 
would not always have to be self-contradictory. Although 
Sigwart's account of double negation rests on this view, 
yet he more cautiously says elsewhere 2 that it is an 
attempted affirmation (' Den Versuch einer Bejahung ') 
against which negation is directed. And this seems so far 
to agree with experience. What is the nature of this 
attempted affirmation ? ' Suggestion ' and ' question ' come 
into the mind as possible equivalents for it. It is difficult 
however to find a special significance for either the one or the 
other on purely logical ground. A question is closely 
related to a command, and has its differentia in being 
addressed to the will of another person. It is impossible in 
good faith to ask a question of oneself. The power of the 
metaphor by which men are said to question themselves 
rests on treating oneself as another person. A question is 
a demand to the will to reveal something known to the 
person whose will is appealed to ; but if I know the answer, 
I need not ask myself ; if I do not, I cannot ask myself. 

A question then as such has not a logical differentia, and 
cannot be the logical presupposition of negative judgment. 
Still it may contain what we want. It is not merely an ideal 
content floating before the imagination, even if we were to 
grant that there are such floating ideas. It is an idea in 
some way tested by Reality. A suggestion seems to be 
the same. It is not a floating content ; it is suggested as 
something, as, so to speak, a candidate for a place in a 
judgment already framed. That is to say, a question or 
suggestion as it is on logical ground, omitting any demand 
upon or incitement to another will, amounts at least to an 
idea whose content is Reality qualified in a certain way. 
Is this all ? This would not suffice to explain the import of 

1 Sigwart distinguishes ' affirmation,' as the conscious opposite of negation, 
from ' Positive ' judgment, as assertion without consciousness of possible 
negation. We shall see in the sequel the value of this distinction, which can 
only be taken as one of degree. 

a Logik, vol. i. p. 120. 

chap. vii.] Negation and Suggestion. 295 

suggestion followed by affirmation or denial. It would not 
explain the significance of the decision even when negative. 
There is something more, and it is this. The content of v 
the suggestion is taken within a whole in which we have an 
interest and which is referred to actual Reality. Every 
suggestion enters into a rudimentary disjunction. I mean 
by rudimentary disjunction an alternative whose limits 
are not made explicit. Where there is a question or sug- 
gestion, there is always a something some general pre- 
dicate known to be true with reference to the matter 
before the mind, and an interest which we have in that 
something. It is within this something that the attempt 
to state it more precisely, the question or suggestion, falls. 
It is hazardous to obtrude analysis on the simpler stages of 
consciousness ; but I do not see how we can have a sugges- 
tion followed by denial cheaper than this. We might even 
fall back on the principle which has been laid down in 
previous discussions, that any consciousness for which a 
continuous real world exists, sustains that world by a judg- 
ment. When a man first doubts and then decides, on 
such a question as whether the river which he sees before him 
is safe to ford, however simple the mental process may be, 
there must be in some form a positive basis of the two 
or more alternatives as well as one suggested alternative. 
He must start with the fact that the river has depth, or 
current, which he must deal with in crossing, and within 
this fact the doubt ' too deep ? ' ' too swift ? ' has its meaning 
for him. In simple cases this embracing judgment of fact 
is hardly traceable except through the interest in the question. 
This interest, if looked at closely, betrays the nature of the 
alternative which the question involves. ' Too deep ? ' 
' What then ? ' 'I cannot get home to-night,' i. e. the 
general fact is that the river is between me and home. 

Negation then presupposes an idea suggested as true of V 
Reality within a state of facts judged to be true of Reality 
and interesting to us in respect of the matter suggested ; or 
in other words, an alternative judged to be true of Reality, 

296 Negation, Opposition, and Conversion, [booki. 

but only so judged as one among a set of alternatives, and 
therefore, in itself alone, problematically judged true of 
reality judged as a possibility, as one among a number of 
alternatives, or as subject to unexpressed conditions. 

We are now able to decide the disputed question whether 
Affirmation is prior to Negation, or whether they are co- 
ordinate types of Judgment. Negation is not, as such, the 
denial of affirmative Judgment, and therefore does not pre- 
suppose the affirmation of that which is denied. So far, 
affirmation is not essentially prior to negation. On the 
other hand, Negation does presuppose some affirmation, 
that is the affirmation of a state of facts which, being judged 
true as a whole, carries with it the problematic affirma- 
tion, the affirmation as a possibility or enunciation as a 
conception in the world of meanings, of the idea ' sug- 
gested.' In this respect, therefore, affirmation is in the 
beginnings of knowledge, at any rate, prior 1 to Negation. 
The world must have positive content judged to be real as 
a condition of anything following from the removal of a 
positive suggestion. But I cannot believe that the con- 
sciousness of a positive world could in fact exist for an 
appreciable time without the development of negation 2 . 
Further, however, it is also true that in the beginnings of 
knowledge negation is a degree more remote from reality 
than is affirmation 3 ; and this character of ideality clings to 
the negative form through its whole development, though 
without debarring it from the acquisition of objective value. 
The remoteness consists in this, that the suggestion which 
denial presupposes is, as we saw, not a mere floating content, 
but a suggested qualification of reality, in short 'a sug- 
gested affirmative relation V An affirmation can be, com- 
paratively speaking, given as fact ; a negation cannot, 
except in quite another sense, be given. It has to be 
made, and made by setting an ideal reality over against 

1 In this sense it may be called, if we prefer to do so, ' positive ' judgment. 

2 See above, Introduction, p. 24, on the formal implication of distinction in 

3 Cp. Bradley's Principles of Logic, p. 116. * See Bradley, ib. 

chap. vii.] Affirmation prior to Negation? 297 

real reality and finding them incongruous. ( That fire is 
still burning' involves no doubt intellectual selection and 
is so far ideal, but ' that fire is not out ' is one remove more 
ideal, because it has to bring up the idea of ' that fire being 
out' and test it by the perceived reality, and then only 
proceed to judge its exclusion to be a fact. We must not 
however exaggerate this difference. Affirmation itself, or 
even positive Judgment, cannot take place until the dis- 
tinction between a mere idea and a fact of reality is recog- 
nised. And with this distinction the idea of negation is 
given. It might therefore be argued that Judgment, not 
to speak of affirmation, presupposes the idea of a negative 
relation 1 ; just as negation presupposes that of an affirma- 
tive relation. The fact seems to be that affirmation pre- 
supposes the idea of negative relation in general, while 
negation presupposes the idea of 2 a corresponding affirma- 
tive relation in particular. This applies to the beginnings 
of knowledge. In complete thought we shall find the two 
more on a level. 

Thus it is true, especially in the beginnings of know- 
ledge, that Affirmation is prior to Negation, both as one 
remove nearer to reality, and as supplying the reality within 
which alone Negation has a meaning. But it is no less 
true that Negation has from the first its essential place in 
knowledge ; and as Reality becomes for us an articulated 
system, the value of negation approaches more and more 
nearly to that of affirmation, with which it finally becomes 
equivalent. This is however not to be understood in the 
sense that the import of negation disappears from know- 
ledge ; but in the sense that affirmation and negation alike 
become double-edged, each involving the other. 

3. Negation then, in its primary shape, is the exclusion Bare denial 
of a suggested qualification of reality. The bare expression judgment. 6 

1 Cp. Bradley, Principles of Logic, pp. 2, no. I find some difficulty in 
reconciling these two passages. 

2 Not ' presupposes a corresponding affirmative relation as j udged true.' 
That view we have rejected. 

298 Negation, Opposition, and Conversion, [book i. 

of this import, reduced to its minimum, would be found in 
what has been called by a mis-translation of Aristotle, the 
infinite judgment. 

The infinite judgment was a term applied by Kant (fol- 
lowing, I presume, the tradition of formal logic) to judg- 
ments which had for their predicate what Aristotle called 
an 'indefinite' or 'undistinguished' name or predication 1 ; 
i.e. such a phrase as ' not-man,' 'not-good,' or the like. 
More important however than Aristotle's expression ' in- 
definite name' was his distinct verdict that such phrases 
were not names or predications. He gave them the title 
of indefinite or undistinguished names or predications, ' be- 
cause they may be truly predicated of everything alike, 
whether existent or non-existent 2 .' It is plain that Aris- 
totle's verdict is right, and that such names have no sig- 
nification. They are ' undistinguished ' because they are 
undistinguishing. It may therefore be observed in passing 
that to attempt to read all negation as affirmation of a 
negative name is an unmeaning device, though possibly 
guided by a feeling of a true ideal, viz. that negation, if 
it is to have a positive import, must involve an affirmative 
element. Only by this contrivance the affirmative element 
is ludicrously absent. We should be, as Mr. Bradley says, 
denying, and then affirming that we have denied. 

It is for this reason that the ' Infinite judgment' may be 
fairly represented by examples in which the denial, though 
undeniable, is unmeaning. 'Virtue is not square,' 'The 
soul is not red,' ' Man is not a stone.' These, qua nega- 
tive, are fully on a level with 'A monkey is not-man,' 
' A stone is not- Christian.' And so in illustrating the 
import of negation we may disregard the pseudo-affirma- 
tive character of the latter instances. Our interest in 
them is that, if strictly interpreted, they display to us the 

1 prjpa or tivopxt aopiarov. 

2 Ar. Uepl 'Epp.. 2. 3. Though the reading is doubtful in the application of 
these words to ovk ovopa, it is enough for our purpose that they are applied to 
ov fifjpa. 

chap, vii.] Bare Negation and Tautology. 299 

nullity of bare denial. ( Not-Christian' literally interpreted 
includes not only heathen humanity, but the fixed stars, 
the sea, and indeed, in Aristotle's words, ' everything whe- 
ther existent or non-existent' except Christians. It refers 
to no one sphere in preference to another, and thus says 
nothing definite enough to be intelligible. The point 
being once established that negation qua negation has no 
significance, we may disregard the attempt to erect it into 
affirmation which draws our attention to this fact. And 
we may then safely take as instances of the infinite judg- 
ment, so far as its import is concerned, the judgments 
typified by ' Virtue is not square.' These show the true type 
of bare denial, for they are the only negative propositions 
in which usage does not irresistibly limit the sphere of the 
negation. And when the sphere is limited, the denial is no 
longer bare. 

Thus it appears that bare denial, whether disguised as 
spurious affirmation, or taken as the mere exclusion of 
mere suggested predicates, amounts in the strict sense to 
nothing. The judgments by which it is typified are the 
exact counterpart of absolute tautology, and like such 
tautology, are not really judgments at all. Identity and 
difference are inseparable aspects of all that exists or can 
be thought ; but in these two classes of would-be judg- 
ments identity and difference fall apart, and thereby the 
conditions of intelligible judgment are destroyed. Pure 
tautology aims at mere identity, and bare negation at 
mere difference. It will be found that any meaning which 
in practice we attach to an apparent tautology or an ap- 
parent bare negation is owing to the introduction of dif- 
ference into the former, or of identity into the latter. 
'Business is business' qualifies a certain class of affairs 
by the principles on which they ought to be conducted; 
'The soul is not a machine' qualifies the soul, not by the 
mere exclusion of mechanical properties in favour perhaps 
of absolute nothingness, but by some positive characteristic 
of the soul which is incompatible with its being a machine. 

300 Negation, Opposition, and Conversion, [book i. 

Significant 3. We have seen that denial was not to be made into 
affirmation by the rough and ready method of the Infinite 
Judgment. But we started, on the other hand, from the 
postulate that denial, as a form of judgment, must be capable 
of contributing something positive to knowledge. Whether 
positive necessarily = affirmative is a problem that will solve 
itself as we come to understand the full nature of negation. 
I use it here simply as antithetical to 'nothing,' or as an 
emphatfc reiteration of ' something.' We must assume with 
Plato that knowledge is the knowledge of something ; and 
if the nature of 'nothing,' as e.g. the abstraction of empty 
thinking, can be known, then nothing is so far and in that 
sense something. 

All significance then is in this sense positive significance, 
and significant negation must therefore convey something 
positive. What is it that it does convey? We shall find 
the answer if we look at that which all judgment has in 
common, viz. the interest or bearing of the judgment. What 
is it that we really mean or wish to predicate when we make 
an ordinary negative judgment? There is always, I may 
observe, something unreal in the analysis of isolated propo- 
sitions. Apart from the context of a book or of a conver- 
sation, or from the precise standards which involve the fixed 
context of science, our interpretation of propositions into 
judgments is almost entirely arbitrary. On the other hand, 
it may be said that in a given context the 'bearing' which 
we ascribe to a proposition is not strictly within the limits 
of what the proposition enunciates, but is read by us into 
its meaning. It may be doubted however whether in actual 
living thought there is any judgment that is not an enthy- 
meme, i.e. an argument with a suppressed premise or a sup- 
pressed conclusion. If we attempt to prune away from the 
judgment all the implied and suggested bearings of the 
proposition which conveys it, we shall find that we have 
whittled away the meaning which is the judgment itself. 
We must never forget the conclusion which we reached 
above, that the unity of the judgment does not exclude 

chap. vii.] The 'Point' of a Jzidgment. 301 

systematic multiplicity within it. The logical content em- 
ployed in any given judgment is a many-sided although 
determinate idea, and is gripped and attached to its actual 
place in the logical mechanism now by some of its promi- 
nences and now by others. Some reservations will have 
to be made in this respect when we come to speak of judg- 
ments that deal with self-contained systems, a type which 
we have more or less anticipated in the individual and 
generic judgments. But in ordinary reflective judging we 
are constantly referred away and away along a series of 
grounds and consequences, and it is idle to attempt to re- 
duce the judgment to simplicity. What we really mean to 
mean is only to be found in the explicit articulation of the 
whole system of fact which the interest of the moment 
covers ; and all ordinary judgment toils after our interest in 
vain. But prima facie the positive judgment has an ad- 
vantage in this respect over the negative. A positive con- 
tent is at all events something ; it is an instalment in satis- 
faction of our interest. If I say that the fire is burning in 
the dining-room, this judgment is no doubt compatible with 
various grounds and various consequences, and in the judg- 
ment as I mean it some particular ground and some par- 
ticular consequence are probably included. Such a state- 
ment would not be made a propos of nothing, or if it were, 
it would be resented just as talking gibberish would be 
resented. There is some point or purpose to which it must 
be taken as contributing, and some reason though possibly 
falling outside the content of the judgment which serves 
as a ground for making it. But over and above all this 
there is, in the affirmative judgment, the positive logical 
content itself, which, though modifiable within very wide 
limits, yet cannot be modified beyond certain limits. The 
judgment may be in praise of some one's thoughtfulness, 
in condemnation of their extravagance, in contempt of their 
effeminacy, or in alarm at their carelessness. But there is 
a nucleus, not indeed fixed nor free from ideal selection 
and synthesis, yet not quite indefinitely variable and 

302 Negation, Opposition, and Conversion, [booki. 

containing a positive element of appeal to normal per- 

In a negative judgment strictly interpreted as mere denial 
this nucleus is lacking, as the consideration of bare denial 
taught us. Therefore we have nothing left but those ele- 
ments of meaning to which the interest of predication is the 
sole clue. Let us take a plain every-day judgment such as 
' A. B. is not a dishonest man/ If we enunciated this pro- 
position in the sense of the infinite judgment, meaning e.g. 
that A. B. is not a man at all, but a stone or a monkey, we 
should unquestionably be held to have violated the conven- 
tions of speech. The meaning of every judgment is to be 
looked for in the attribute to which is attached the interest 
that guides the selection of the content used in judging. 
But this attribute must obviously have definite relations, at 
any rate for some special purpose, to the content affirmed or 
denied. Whether it can precisely coincide with the content 
affirmed is a point to which I shall have to recur ; but it cannot 
precisely coincide with the content denied, for if so, no result 
in which we had an interest would spring from the denial 
the whole reason of our interest would be cancelled and be put 
away with the denial of the attribute on which it centred. 

Now I maybe interrupted at this point with the objection 
that this is exactly what is always happening in negation. 
When we have suspected a man or thing of having some 
attribute which interests us, and then find that we were 
mistaken, our interest in the individual may, and often does, 
fall dead at once. A man may be pointed out to us in a 
crowd as about to be our fellow-traveller on a difficult 
journey, and we may regard him with some interest on that 
account ; but if we learn that it was a mistake, and that we 
have nothing to do with him, we shall probably after that 
regard him as 'nothing to us.' This is in fact almost a 
recurrence to the infinite judgment; for though we must 
know that he is a man, yet so long as he is not to be our 
fellow-traveller we do not care whether he is alive or dead ; i. e. 
for any positive quality of his humanity. The judgment ' he 

chap, vii.] Content of Denial. 303 

is not coming with us ' approaches then to a judgment of 
bare exclusion, the attribute in which we have interest being 
the attribute excluded. 

In the first place, I think, we must to a great extent 
admit this contention ; and simply refer it to a difference 
of degree. Negative judgment does begin with a phase 
inappreciably differing from the infinite judgment. But 
yet, of course, the question ' Coming with us ? ' must have 
originated in some such judgment as ' He is the sort of 
person who might be coming with us ; ' and it is within 
this fact judged true that the ultimate negation ' not 
coming ' has its meaning. The interest is first awakened 
by the whole attribute ' such as to come,' and could never 
have been aroused but for the presentation of such an 
attribute. If the negative judgment were really one of 
bare exclusion it would apply equally well to everything in 
the world, and no interest would have been aroused which 
could have led us to make it of a particular individual. But 
in the second place, it must be added that in as far as, in 
the alternative which formally arises within the attribute 
'such as to come,' all the interest practically falls on one 
side of the alternative, this is an actual defect of knowledge 
and morality ; but has not, in the case supposed, been 
pushed far enough to prevent the insistance on the positive 
attribute ' capacity to come V And this attribute supplies 
in fact a positive content for the denial, though we by the 
hypothesis happen to be now indifferent to it. The denial 
really contains the judgment, 'The man is one who, we 

1 It is a commonplace satire to say of a man that the universe interests him 
only in as far as it is what his particular whim requires. What is not money, 
or total abstinence, or woman's emancipation, as the case may be, is nothing to 
him. This is a good illustration of the moral and intellectual impotence indi- 
cated by any approach to bare negation. Hegel has quaintly compared the 
distinction between bare and significant denial to that between crime and civil 
dispute. If I steal, my act says This is not yours,' without asserting that it is 
mine or any one's by right, i. e. it ignores the whole sphere of property or 
reasonable possession by alleging no ground for its denial. In a civil dispute 
I say ' This is not yours, because it is mine/ i. e. I assert rights of property, as 
you do ; but I deny your right on the ground of mine. 

304 Negation, Opposition, and Conversion, [book i. 

thought, might come, but is not coming.' The proximate 
case in the ascending scale of knowledge may be illustrated 
by supposing that instead of our interest dropping dead on 
hearing that he does not come with us, this negative judg- 
ment enunciates to us a regret that he is not coming, 
implying that we ascribe to him some positive quality which 
causes us to regret losing his company. In this case the 
positive bearing of the negation ' He is not coming with us ' 
is primarily a consequence of the negation operating upon 
the judged content ' We should wish him to come with us/ 
This consequence supplies the denial with a positive import, 
and may be the only aspect of it prominent in the mind. 

But there is something else to be considered. Every 
judgment without exception challenges the question 
' Why is it so ? ' or at least 'How do you know it to be 
so?', the former question demanding the cause or real 
ground, the latter demanding the cause of knowledge or 
logical ground. The*se two kinds of ground run into one 
another, as we saw, and need not be distinguished for our 
present purpose. In denial, then, there must be this 
element also of positive import, the attribute which justifies 
the denial for us. It is plain further that in case of the non- 
existence of the immediate or apparent subject, this attri- 
bute may be judged directly of Reality, which is the ultimate 
subject in Negation as in all Judgment. ' The house on the 
marsh is not burnt down ' may be true because there is no 
house on the marsh, and although reality positive fact 
excludes the burning down of any such house \ 

Thus in Negation we have two positive elements which 
may be present together, or in various relations of promin- 

1 It may be objected that in such a case to say ' The house on the marsh is 
burnt down,' is not so much false as unmeaning, in other words that the nega- 
tive * the house is not burnt down/ has meaning only if there is a house, and 
presupposes or asserts that there is one. I have strong sympathy with this 
objection, which turns on the problem of a real distinction between subject and 
Predication within the Judgment. But an unmeaning judgment is clearly not 
true. The only doubt is whether its not being true justifies any negative except 
one which should brand it as unmeaning, e. g. ' There is no house to burn down.' 
The more hypothetical judgments are, the less they present this difficulty. 

chap, vii.] Positive Basis of Negation. 305 

ence, or may wholly or partially coincide. The third 
element of import, the positive content explicitly employed 
in judging, falls away in the negative judgment, being 
replaced by a bare exclusion of an explicit content. This 
bare exclusion is what we discussed on its own merits in 
the second section of the present chapter, and found to 
amount in itself to nothing. We are therefore referred for 
the meaning of significant negation to the positive ground, 
or positive consequence, of the exclusion which forms the 
outward and visible shape of negation. Thus we approach 
the solution of the problem how knowledge can take the 
form of ignorance how ' what it is ' can be known through 
knowing ' what it is not.' 

The primary analysis of the significant negative judgment 
presents therefore a close parallel to that of the hypothetical 
judgment. ' A is not B ' may always be taken to = ' A is x 
which excludes (or which is implied in excluding) B/ Or 
in extreme cases we may have ' Reality is x> which excludes 
or is involved in excluding A B.' Just thus we saw that ' If 
A is B it is C ' may always be interpreted into ' A is a factor 
in a real system x which given A B involves C ; ' or in 
an extreme case, ' Reality contains a system x such that, if 
A B were placed within it, C would result.' We examined 
at length the conditions under which such a relation as 
that enunciated in the hypothetical judgment could be 
made intelligible, and we found that a real system within 
which the separate terms should be interdependent was the 
bond of union which alone could justify such a reference of 
one thing to another. In the same way we saw that nega- 
tion presupposes a real system a system affirmed in judg- 
ment to be actual as a condition of its intelligibility; and 
if it is replied that a system presupposes negation for it 
presupposes difference we must answer, first, that negation 
in its pure form as simple contradiction is the abstraction 
of difference, and may be later in origin than, or at least 
presupposes as coeval with it, the positive differences which 
all thought involves ; and secondly, that in thought it is 

VOL. I. X 

306 Negation, Opposition, and Conversion, [book i. 

possible and indeed is the rule for factors to presuppose 
each other, and to grow into distinctness pari passu. In 
fact, Negation is simply the logical, conscious expression of 

Significant negation, then, like hypothesis, is intelligible 
within and with reference to a system judged to be actual. 
It is only within such a system that something can be made 
out of nothing by implying a positive ground or conse- 
quence in a bare denial. In other words, the essence of 
formal negation is to invest the contrary with the character 
of the contradictory, or to raise mere discrepancy or posi- 
tive opposition to the level of the absolute or contradictory 
alternative which is the abstraction of difference. It is only 
contradictory negation which allows a conclusion to be 
formally drawn from the negative ; contrary negation does 
not admit of this. It is only contrary negation which 
allows any import to be materially attached to the nega- 
tive ; contradictory negation does not admit of this. The 
fact that contrary negation can be given the force of contra- 
diction, that a positive opposite can be known as a sole 
alternative, and that unless this is done knowledge remains 
inarticulate and chaotic, is simply the fact that Reality is a 
system. It is in considerations of this kind that we must 
look for a reconciliation of conflicting ideas as to the 
'subjective' or 'objective' place of negation. We must 
ask in every case what negation ? The negation of what 
and under what presuppositions? Without going further 
into extreme views about the objective import of nega- 
tion, I am most anxious to persuade the reader that the 
fruitful question is not ' Can we conjure a meaning out of a 
bare denial?' but ' Why is it that in knowledge we cannot 
do without denial ? ' 'In your " system of differences," ' it 
may be said, ' you put a significance into your negations, 
and then pride yourself on finding there what you put in.' 
This is true. What I want to insist on is the fact that this 
kind of significance cannot be put into anything but nega- 
tion, and the light which this fact throws on the significance 

chap, vii.] System and Negation. 307 

in question. Reality is a system, and you cannot have 
system apart from negation. This is the central fact from 
which all enquiry must start. The connecting link between 
difference, contradiction, and contrariety 1 is that difference 
becomes contradiction when taken as mere difference or 
as the abstraction of difference, that is, as expressed in 
a negative judgment which (like the infinite judgment) 
professes merely to exclude a given idea, or deny a given 
affirmation. If the denial were within a self-identical 
system it would carry a positive bearing. As ex hypothesi 
it has no positive bearing, it embodies mere difference 
without identity, or the abstraction of difference. Such a 
denial is the pure contradictory of the affirmation which it 
denies. On the other hand, difference becomes discrepancy 
or contrariety when not the formal abstraction of differ- 
ence, but positive differents claim the same place, and the 
same place means the same relation to the same system. 
Such contrariety exists between 'A is B/ and * A is B 2 .' 
Thus the articulate arrangement of differences under their 
systematic relations is the root of positive discrepancy. 
The system as determined by one relation excludes, under 
that relation, the system as determined by any other ; 
and the system as a whole identifies any one of its positive 
relations with the mere difference from, i. e. the bare 
exclusion of, certain other positive relations. A is either 
B x or B 2 . This is the combination of Contradiction and 

It is not essential that the positive ground and positive 
consequence of a denial should be different. Under 
conditions of precise knowledge they must be the same. 
We shall see that where only two alternatives are 
possible, and they exclude one another, either of them 
is denied by the affirmation of the other, and affirmed 
by its negation. Under such conditions the denial of 
one alternative has the affirmation of the other both for 

1 See below, Book II. chap, vii, on the ' Formal Postulates of Knowledge.' 

X 2 

308 Negation, Opposition, and Conversion, [book i. 

its ground and for its consequent. * He will either dissolve 
or resign ' permits us to understand under the denial 
'he will not resign' the affirmation 'he will dissolve' alike 
as its ground and as its consequent. It is plain that in 
actual knowledge there are degrees of this coalescence. 
The ground may be imperfect or extraneous ; it may be 
replaced by any positive quality that excludes the predi- 
cate denied, i. e. in this case, excludes resignation. This 
positive quality might be even difficult to formulate pre- 
cisely, and might run as close as possible to a bare denial ; 
we might feel sure that ' he is not the man to resign ; ' 
which means that his general character as we understand it 
precludes the idea that he will resign. Such a general 
ground would be at once reinforced in its cogency and 
restricted in its result by the consequence of the denial, 
the necessities of the case being as supposed above. The 
two in their coalescence, ' he is a man who will not resign,' 
and ' not resigning, he must dissolve/ would in that case 
form the complete analysis of the denial * he will not 

It has been necessary in this discussion to anticipate the 
account of disjunction which will be given in the next 
chapter. Perfect disjunction is of course a late form of 
knowledge. But it is an ideal inevitably involved in the 
nature of negation. All significant denial all denial, that 
is, which rises above the level of the infinite judgment 
corresponds to this ideal in two respects at least. Every 
denial has its meaning within an attribute or set of attri- 
butes judged to be real ; and every denial affirms some 
positive matter which affects and is affected by its relation 
to such a comprehensive attribute. This may be illustrated 
in another way, which will also serve as a recapitulation of 
the stages of negation. 

Negation is rooted in the fact of difference, but difference 
is not enough to warrant negation. Mortality is a differ- 
ence within the identity of man, but we do not therefore 
deny that man is mortal. Significant negation begins, we 

chap, vii.] Negation implies Contradiction, 309 

said, when positive differents claim the same place in the 
same system in the simplest case, when differents claim 
to be identical. Man is not mere mortality, i. e. does not 
coincide with mere mortality in the system of reality. As 
thus conflicting, which of course can only happen in a 
judgment, differents are contraries or opposites, and the 
assertion of one is the negation of the other. Now these 
contraries or opposites may be of any number. There is 
nothing to limit them. Any colour is the contrary or 
opposite of black, if asserted in the same relation ; and so 
would any sound or taste be, if asserted in the same rela- 
tion, which seems impossible for a sane man. If then we 
consider negation at this stage as embodying contrary 
opposition, what follows from it ? ' This surface is not 
black ' has indeed a ground, viz. that it is some particular 
other colour ; but what about the consequent of the nega- 
tion ? There is none, except that the surface is some colour 
other than black, and therefore we lose by choosing the 
negative expression rather than the positive, and the signi- 
ficance of the negation qua negation is absent. What 
follows from the absence of a consequent as definite as the 
ground ? Nothing less than this, that negation cannot be 
explained on the basis of mere exclusion of contraries. It 
is indeed possible to deny intelligibly on such a basis, in 
virtue of the general consequence of negation, but no 
reason can be assigned for in such a case preferring nega- 
tion to affirmation. For in the case supposed we should 
be concluding from ' A is red,' through 'A is not black,' to 
1 A is of some colour other than black ' a manifest loss. 

Negation can have no bearing, i. e. no interest or raison 
detre, unless the contraries are limited so that something 
follows from the negation. In other words, Negation 
always involves Contradiction between contraries and not 
merely Contrariety. There may be any number of alterna- 
tives, but unless the number is limited or falls within some 
positive characteristic however vaguely known, nothing can 
follow from the denial either of one or of any number among 

310 Negation, Opposition, and Conversion. [Booki. 

them. Therefore though negation originates in difference, 
which it raises to contrariety by embodying it in definite 
relations, and though it does not arrive at formal contradic- 
tion between opposites till long processes of thought and 
language lie behind it, yet I am unable to comprehend how 
any negation can have interest apart from being taken 
within a positive whole, however vague, which is of the 
nature demanded by the relation of contradiction when 
established between opposites. Mere contradiction as 
between * he is good ' and he is not good ' is given in the 
nature of negation from the first ; and its development 
consists in filling this unmeaning form with significant 
opposites, so that from ' he is not good ' we may be able 
to infer something more than that ' it is not true that he is 

Significant Negation then combines in itself the absolute 
Contradiction which was illustrated by the Infinite Judg- 
ment, and the Contrariety which arises between differents 
when referred to the same place in the same system. 
Without contrariety negation would have nothing that it 
could mean, but without contradiction it would not have in 
itself the power to mean anything. 
Opposition 4. The rules of the opposition and conversion of Judg- 
versiorTof ments > which have come down to us almost as Aristotle 
Judgments, formulated them, are founded on the classification of judg- 
ments according to ' quantity.' They therefore lay down 
the relations to one another of all classes of judgments 
which this principle recognises, in as far as the truth or 
falsehood of any one judgment affects the truth or falsehood 
of any other which deals with the same content. But 
when we attempt, as we have attempted above, to distin- 
guish the kinds of truth which various types of judgment 
embody, then the relations between the various classes 
of judgment cease to be a matter of mechanical rule-of- 
thumb, although not hard to understand if we pay attention 
to the actual significance of the judgments with which we 

chap, vil] Singular and Plural Judgments. 3 1 1 

i. The principle from which we must set out is that every- Opposi- 
thing which can be affirmed can also be denied. In some tlon ' 
cases the denial will be confined to a shape closely corre- 
sponding to that of the affirmation, and in some there will 
be two kinds of denial which will fall apart. 

a. The Singular Judgment cannot be treated for the Between 
present purpose as a case of the universal. It has, as judgments 
we saw, a universal character, but not in the sense of re- 
ferring to an aggregate of individuals. If ' Caesar crossed 
the Rubicon ' is true, ' Caesar did not cross the Rubicon ' 
is false ; and if the negation is false the affirmation is true. 
Thus the relation of Contrary Opposition, according to 
which the Universal Affirmative and the Universal Nega- 
tive of formal logic may both be false, falls away in 
the case of a Singular Judgment in our sense of the term. 
In this type of judgment we have the simple relation 
of affirmation to formal negation which is contradictory, 
i.e. presents an absolute alternative. The reason of this 
we shall have further to consider in treating of Double 

/3. The Judgments of Enumeration, Plural or Particular Between 
Judgments, including the Collective Judgment, present the judgments 
relations towards each other with which we are familiar 
in the common scheme of opposition. The peculiarity of 
these relations is that in them an absolute alternative or 
contradictory opposition is only to be obtained by opposing 
judgments of different quantities. The reason of this is 
well brought out in a phrase which Aristotle employs in 
his account of opposition, where he states the contradictory 
of 'All are' to be 'Not all are' instead of using the 
expression of our text-books ' Some are not ; ' or when 
he says that the contradictory of a proposition which 
affirms a predicate universally, is one which asserts that 
of the same subject the predicate is not universally true. 
What is affirmed in a collective judgment is the homo- 
geneity in a certain respect of an aggregate still regarded 
as an aggregate of enumeration, although endowed with 

312 Negation, Opposition, mid Conversion, [book i. 

sufficient unity to warrant itself as a completed whole. 
The denial of the judgment is the denial of this homo- 
geneity, and is rather a consequence of than identical 
with the partial counter- enumeration which our logic- 
books take as its type. If, for instance, we assigned 
a number to the counter-enumeration, the contradiction 
would no longer be complete, and we should find ourselves 
in contrariety instead. To say that ' All these books are 
German ' and that ' Two of them are not ' cannot be a 
contradiction pure and simple ; for the falsehood of ' All 
these are ' is compatible with the truth of ' Two three 
or all of them are not.' This is enough to show that 
1 some not,' if we take it as a sign of counter-enumeration, 
is less safe in contradictory opposition than ' not all.' 

As regards the ' contrary ' opposition of ' All are ' and 
' None are,' the doctrine of formal logic is true so long 
as we confine ourselves to Judgments of Enumeration. 
' None are ' asserts a complete counter-enumeration or its 
equivalent based on some other ground, and besides this 
assertion and its contrary there are as many alternatives 
as there are individuals in the aggregate, minus one. 

The particular or incomplete collective judgments ' Some 
are' and 'Some are not' (sub- contraries) are of course 
compatible with each other so long as we do not determine 
them numerically; and continue to be so then if we consider 
that incompleteness of enumeration debars us from all 
reference to a sum total. If on the other hand we permit 
the comparison with an assumed sum total, we pass at this 
point into calculation. The general conception under 
which we are enumerating always, it must be remembered, 
implies a total ; so that calculation lies very near to judg- 
ments of this type. ' Six men were killed and ten wounded 
(but not killed) ' are judgments perfectly compatible with 
one another if the number of men on the ground was six- 
teen or more ; but if there were only fifteen or fewer, then the 
two judgments at once rise into contraries. Both may then 
be false, but one must be. This however is calculation. 

chap, vii.] The effect of Exceptions. 3 1 3 

This account of the matter includes all that need be 
said of the Singular judgment if used in opposition to 
the Collective judgment. In such a case the Singular 
judgment takes the place and follows the rules of a 
judgment of Enumeration. It must however undergo 
a transformation, even if only implied, in taking on a 
relation to the basis of enumeration. ' How many Liberals 
voted against the Bill?' A. B. did, C. D. did,' &c, &c. 
These singular propositions are read off into enumerative 
judgments, ' One Liberal, two Liberals,' &c. 

The further judgments which arise out of the Judgment 
of Enumeration and Measurement follow the characteristics 
of those forms of the true universal judgment to which, 
whether as generic or as hypothetical, they severally 

y. I will now point out shortly the characteristics of these Between 
judgments themselves when placed in opposition. The j^^nts 
tendency of the higher stages of knowledge is, as we saw in 
the last section, to fuse contrariety and contradiction into 
one. This is obvious, for instance, in the individual generic 
judgment, for the same reason as in the singular judgment 
itself. And even in the analogical judgment the tendency 
to fusion is strongly marked. The allegation of exceptions 
against a generic character, whether in form of expression 
positive or negative, must either be insignificant as when 
the exceptions are apparent and not real, or else tend by 
analogy to establish a contrary alternative or positive 
contradictory. In the former case the judgments which 
emphasise the exceptions must be taken to be not generic 
judgments at all, but mere enumerative judgments, which 
therefore cannot touch the essence of the generic judgments 
they appear to oppose. For we shall find the dominant 
principle in these relations to be that a judgment of one 
type a cannot deny a judgment of another type /3 ; although 
the former may suggest a judgment of the type )8 which 
will constitute a full denial of the other judgment of 
that same type. Under the head of such mere enumerative 

3 1 4 Negation, Opposition, and Conversion. [Book i. 

judgments would come all observations of artificial forms, 
mutilations, abortions, etc. in organic and spiritual beings ; 
and all accidental juxtapositions rendered by judgments 
whose subjects have no connection with their predicates. 
The generic judgment ' Man is a creature with a sense of 
justice' is not invalidated by instances drawn from dead 
men, lunatics, or idiots ; nor even, perhaps, from criminals, 
if there are such, whose conscience is obliterated by life- 
long war with society. But I shall be told that a scientific 
law has no exceptions. This is just what I am maintaining ; 
I am saying that exceptions are either apparent or real, and 
in the former case, that now before us, do not deny the law; 
in the latter proceed positively to indicate another law. In 
the second case, when the law is really impeached by the 
bearing of the exceptional instance, this bearing must have 
a positive import, which may not amount to a suggested 
law, but must be in the same region of essential indi- 
viduality in which the characteristic that is denied has its 

If I say that all exogenous trees are dicotyledonous, 
I am opposed by a real, not merely apparent, exception in 
the case of the Coniferae, which though exogenous have in 
many species more than two cotyledons. Here we have 
one Generic judgment (I use 'generic' in the logical sense 
which I have explained) opposed to another. It is not 
merely that here and there an aborted or mutilated in- 
stance is to be found in which a part of the plant is want- 
ing; but that an enormous natural order with marked 
unity of habit, and in the strictest sense * sharing the 
characteristic on which the analogy is based, does not 
display the character required by analogy. Now I am 
not aware that any importance has been attached to 
determining the connection between exogenous wood- 

1 Here an error is possible. The wood-formation of Coniferae, though pro- 
ceeding from a cambium ring outside the old wood, has differences from that 
of Dicotyledonous Exogens. If these differences were of importance the excep- 
tion might break down as not a case under the rule, Coniferae not being true 

chap, vii.] Generic Judgment how upset. 315 

formation and the number of seed-leaves or cotyledons ; 
but it is plain that the conflict of generic judgments so far 
as we have followed it does not destroy the idea of such a 
connection, which would be the effect of a mere contra- 
diction, but suggests that it may be characteristic of plants 
with two or more seed-leaves. Supposing that monocoty- 
ledons were also found in some cases to form wood ex- 
ternally, the question would still arise whether any principle 
of development could be traced according to which the 
characteristics under discussion might arise together or 
owing to connected causes, as if e. g. there was a point at 
which the one natural kind approached very close to the 
other. If so, the supposed further exception would still 
lead to a positive principle or contrary, and not to an empty 
contradiction. Even if the first generic judgment were a 
sheer blunder and confusion, as has been the case from 
time to time with judgments propounded in science, it is 
scarcely possibly to rectify the confusion except by substi- 
tuting for it the true positive conceptions that arise out of 
the cases which overthrow it. An example in point is 
Ehrenberg's inclusion of a group of confervoid Algae (Vol- 
vox) under the class of Infusorial Animalculae, or again, 
probably, his alleged detection of highly-organised struc- 
ture in the Infusoria proper. Enumerative exceptions are 
futile in such cases ; what is needed is a re-interpretation 
of the character of the group as such. Such a re-interpre- 
tation is at once contrary and contradictory to the mis- 
taken judgment which it corrects. But in the process of 
interpretation it may and perhaps must pass through a 
stage which may best be described when we are speaking 
of the hypothetical judgment. 

h. The contrary of the Hypothetical Judgment is as usual Between 
a judgment of the same type. The complete contrary of thecal 
' If outdoor relief is refused the workhouses are crowded ' Judgments, 
would be ' If outdoor relief is refused the workhouses 
(caeter is paribus) are not crowded.' This denial means that 
the condition expressed in the hypothesis ' If . . refused ' is 

316 Negation, Opposition and Conversion, [bookt. 

not merely inoperative to cause pressure on the workhouse, 
but is actively operative to decrease that pressure. I insert 
the limitation caeteris paribus merely to secure the judgment 
being taken as truly hypothetical, because in such concrete 
matter as this there is a tendency to interpret the judgment 
as collective in the sense that ' Every case of a is a case 
of (3 ;' so that it may be objected to on the score of acci- 
dental instances. In abstract matter, e.g. in geometry, 
where the hypothetical judgment has an unambiguous 
import, these objections are understood to be inadmissible. 
Parallel lines are taken qua parallel when it is said that they 
do not meet, and so forth. 

This contrary is the form of negation to which all precise 
thought aspires. If the condition is irrelevant and wholly 
unconnected, then indeed the entire type of knowledge to 
which we have aspired is a delusion and a snare, and the 
mere contradictory which will express our ignorance must 
be found in a judgment of a lower type. But if the con- 
dition is relevant it must operate somehow, and we can 
only choose between one view of its operation and another. 
Such a choice is expressed by embodying mere contraries 
in an absolute alternative or contradictory ; by considering 
'If A is B it is not C as the contradictory of 'If A is B it is 
C ;' as it is the only way of denying it by a hypothetical 

But if we are to destroy the hypothetical judgment itself 
as an expression of ground and consequence, we must aim 
our negation precisely at its form. The enumerative parti- 
cular would not help us here. When we have said that 
' If (i. e. in so far as) a man is good he is wise,' it is idle to 
reply that some good men are not wise. This is to attack 
an abstract principle with unanalysed examples. What we 
must say in order to deny the above-mentioned abstract 
judgment is something of this kind : ' If,' or 'Though a man 
is good, yet it does not follow that he is wise,' i. e. ' Though 
a man is good, yet he need not be wise.' The particle 
' though ' introduces the condition as a supposal, but by its 

chap, vii.] The Modal Particular. 317 

adversative force prepares us for a denial that it has any 
connection with the consequent. 

This same form, which may be called the modal particular, 
is the appropriate contradictory to a generic judgment which 
has to be altogether surrendered and cannot be corrected by 
a positive contrary. Its meaning is however not as clear as 
that of the Generic or Hypothetical judgments. For it does 
not assert a positive relation, but drops down into an un- 
analysed quality of exclusion, and thus into the confused 
concrete of phenomena. It may therefore mean that the 
supposed condition is inoperative and irrelevant, or it may 
mean that it is weakly operative and liable to be overcome 
by normal counteracting conditions, or that it is operative 
as asserted in the hypothetical judgment, but liable occa- 
sionally to be overcome by exceptional conditions. This 
last is a common meaning, but is not the true negation of 
the opposed abstract hypothetical judgment, and ought to 
be discarded from science, though there is no means of re- 
lieving the modal particular negation from it. How then 
are we to treat the correlative case, in which we deny ' If A 
is B it is not C ' by ' Though A be B yet it may be C ' ? 
This seems to confirm our view that the character of mere 
negation is incompatible with that of the hypothetical 

judgment. For the former of these two contradictories is 
of course the same judgment which we have already con- 
sidered in the light of a contrary and positive negation ; 
and the latter seems therefore to retain under its affirma- 
tive form the essential character of mere denial. ' Though 
A is B yet it does not follow that it is not C ' expresses the 
only sense in which the affirmative modal particular is a 
true or mere contradictory to the negative hypothetical 
judgment 1 . This sense is not in itself satisfactory if taken 
as the import of possibility, and real possibility demands a 
nearer advance towards the affirmative contrary a recog- 
nition of some real operative condition making for the 
connection alleged possible. That this is so only confirms 

1 See below, on Privation and Affirmation. 

3 1 8 Negation, Opposition, and Conversion, [book i. 

the suggestion made above that in significant negation 
contrary and contradictory tend to become one. 

I may anticipate the case of Disjunction so far as it 
here concerns us by saying that the denial of a. disjunctive 
judgment, though formally possible, is not a problem that 
naturally arises in logic. The disjunction is the pre- 
supposition and the goal of negation as an organon of 
knowledge. By denying it as a whole we sweep away the 
fabric of knowledge relative to the matter in hand, and 
must begin over again from the beginning, as there is no 
sphere left within which anything can arise from the denial 
of the disjunction. To deny a disjunction in this sense we 
should not trouble ourselves with the alternatives, but 
analyse them into their common basis and deny that. An 
impersonal judgment, as expressing wholly inarticulate 
knowledge, is the appropriate form for such denial, unless 
we are denying one disjunction under another. ' The soul 
is neither square nor round ' may be denied by ' The soul is 
not in space ; ' for this denial has a positive ground and 
consequence founded on an implied disjunction, 'either in 
space or intellectual.' But if we are presented with a 
number of alternatives about a matter which seems to us 
to have no basis in reality nor relation to actual knowledge 
at all, then we may reply with the impersonal negative as 
the form of thought most suited to mere absence of positive 
content. ' The disembodied spirit in its earthly presence is 
revealed either by contact or by signs.' To this an entire 
unbeliever would probably answer, ' There is no earthly 
presence of disembodied spirits,' and here he approaches, 
not wholly by his own fault, the infinite judgment. He 
has merely said that reality is without the matter alleged, 
and his saying has no positive import beyond what arises 
from the imputation to reality of a character whatever 
that may be not necessarily incompatible with, but 
rather undistinguished by, the presence of disembodied 

Specific denials of a disjunction on the ground of incom- 

chap, vh.] Inference from Falsity. 3 1 9 

pleteness or superfluity 1 are of course either under a further 
disjunction which the denial tends to make explicit, or in the 
second case, prima facie, under the disjunction to be denied 
itself, with the result of excluding one of its alternatives. 

ii. In treating of the contradictory relation, that namely Double 
between two judgments of which one simply denies the Ne 2 atlon - 
other, so forming an absolute alternative, we saw the results 
that spring from double negation. We appealed to double 
negation for instance in the case of the singular judgment, 
such as ' Caesar crossed the Rubicon.' This, with its simple 
denial ' Caesar did not cross the Rubicon,' forms an absolute 
alternative, although the denial has a meaning and is not a 
mere infinite judgment. So far as this is the case, the oppo- 
sition between the two is at once contrary and contradictory. 

Do the two cases of inference from falsity in contra- 
dictory opposition stand on the same footing ? The one is 
from the falsity of the affirmative, the other from the falsity 
of the negative. The former amounts to single, and the 
latter to double negation. 

The explanation of single denial which has been given 
above may be briefly restated here. The abstraction of 
difference, taken in respect of its contrast with identity, 
and so as mere non-identity or otherness, is employed 
in negation as the vehicle of a positive contrary, which 
contrary is thus invested with the full alternative force 
that belongs to otherness as such when contrasted in the 
abstract with sameness as such. As regards the history of 
early thought on this question, of course we are not to 
look for determinate abstractions in primitive minds. But 
primitive minds probably are abstract, though they do not 
deal with abstractions. We must look for the germ of 
contradictory negation in mere repugnance or repulsion, 
which, although a positive state, has a peculiar aspect of 
negativity to which the inarticulate abstractness of the 
primitive mind lends an aspect rather of contradiction 
than of contrariety. Every one who has watched children 

1 See following chapter on this case. 

320 Negation, Opposition, and Conversion, [booki. 

must have noticed the remonstrant ' No ' without any 
expressed content, which is a sign of aversion to something 
done or suggested. The absence of indicated reference to 
any particular matter is often surprising, and impresses an 
observer by the difficulty of finding either the bearing or 
the ground of the negation. Here it is rather the positive 
contrary that is undeveloped and latent than the mere 
rejection or contradictory. Therefore I cannot but think 
that the absolute alternative mere generalised otherness 
or rejection makes itself explicit by the side of the 
positive contrary at a very early stage of thought. 

Thus though I do not take every negation to be neces- 
sarily aimed against an affirmation of the same content, yet 
it seems to me that the pair of judgments which form 
a contradictory opposition embody an ultimate fact of 
knowledge. Single negation is in form the substitution 
of mere difference, or nothingness, for the combined identity 
and difference which alone have meaning. This form is 
the basis of the alternative in contradiction. It is the 
alternative antithesis between something and nothing. 
That 'nothing' is furnished with a meaning in hunc 
effectum does not appear from or affect the form of 
contradiction. Single negation, then the passage from 
the falsity of 'A is B' to the truth of 'A is not B '- 
must be regarded on its formal side as the abstraction of 
a universal characteristic of knowledge. It means that 
A is, under the conditions and for the purpose of the 
judgment in question, in a relation of pure otherness 
to B. 

The case of double negation the passage from the 
falsity of ' A is not B ' to the truth of ' A is B ' is in my 
judgment accounted for by the preceding remarks. The 
true problem, to my mind, is not how negation should be 
the absolute alternative of the corresponding affirmation, 
but rather how, being in its exterior form and vehicle such 
an alternative, it should become possessed of positive 
intelligible import. The fundamental nature of negation, 

chap, vii.] Negation as Alternative. 321 

thus understood, may no doubt be embodied in the prin- 
ciple of Excluded Third or Excluded Middle, which asserts 
that of two contradictory enunciations one must be true 
and the other false. Thus stated, the principle is merely 
formal, because the question immediately arises, 'What 
are contradictory assertions?' The definition might be 
made plainer by substituting for the phrase in question an 
expression such as 'the assertion and denial of the same 
content ; ' but no definition can relieve us from the task, 
which I have attempted to perform in this chapter, of 
explaining what a mere denial of an assertion really is. 
Excluded Middle is thus merely the abstract case of 
Contradiction or simple negation, and the proof of the 
principle lies in the analysis of negation. 

I may illustrate this view, in the case of double nega- 
tion, by two conceptions that deserve attention. Sigwart 
ascribes the affirmation that admittedly results from double 
negation to the reappearance of an original affirmation at 
which the first negation must have been aimed, so soon as 
that first negation is cancelled by the second. I take this 
view to be true in substance, but false in the fact which its 
expression postulates. It was pointed out above that 
not every negation presupposes an affirmation, and that 
Sigwart himself, when not treating of double negation, 
more correctly postulates as the condition of denial only 
an attempted affirmation. But it is true, and this is probably 
what Sigwart meant to convey, that every negation bears 
on its face the nature of an alternative, so that, though we 
may not in fact have proceeded to it by denying an explicit 
affirmation of the same content, we are yet able to go 
from the negation of one member to the establishment of 
another. It is one thing to say that every negation is 
preceded by a corresponding affirmation, for we may not 
have judged on the subject at all, but quite another to say 
that every negation bears on its face that, if we judge, it is 
the sole alternative to the corresponding affirmation. This 
principle appears to me to be of the essence of the matter. 
VOL. I. Y 

322 Negation, Opposition, and Conversion. [Booki. 

It is this that gives double negation its distinctive precision 
and emphasis. 

In opposition to Sigwart's idea, erroneously expressed as 
I admit it to be, of re-establishing an original affirmation, 
Mr. Bradley has maintained that the warrant of double 
negation simply consists in this, that in order to deny 
a negation we must already be in possession of the corre- 
sponding affirmation. We can only, he contends, deny A 
is not B on the ground that, within our knowledge, A is B. 
This allegation is made with good reason. We can indeed 
deny A is B on the ground that A is x or y, each of which 
excludes B ; but we cannot assert A is B on the ground 
that A is not x or y, each of which excludes B. We 
cannot deny the consequent not-B on the strength of 
denying the antecedent x or y. The old rule of the 
hypothetical judgment, 'Affirm the antecedent or deny the 
consequent,' forbids this. 

But on looking closer we shall observe that this impos- 
sibility is based on the imperfect view of the hypothetical 
judgment which assimilates its rules to those of the judg- 
ment of enumeration. This view disregards the possibility 
of a connection at once synthetic (i. e. not tautologous) and 
pure (i. e. free from irrelevancy). For in this case the denial 
of the condition is the denial of the consequent ; and it is 
this which has been before us throughout as the essential 
and ideal meaning of judgment. This assertion of a pure 
connection between condition and consequent becomes, in 
the case of a negative consequent which is now before us, 
identical with our position that all intelligible negation 
takes its meaning from contrariety, though its form may 
be that of contradiction. To say that in ' If A is x it is not 
B' we cannot go from ' not x' to ' not not-B ' (i.e. to B) is to 
say that there cannot be contradictory opposition between 
contraries \ 

1 The negative character of not-B might cause a difficulty, but is not in dis- 
pute here. What is disputed is the possibility of getting to anything by denying 
that A is x in the judgment ' If A is x it is not B.' 

chap, vii.] The value of Double Negation. 323 

Contradictory opposition between contraries can of course 
exist only if the possibilities are limited by means of a 
disjunctive judgment, and in this case Mr. Bradley admits 
that the double negation may be got at otherwise than by 
the corresponding affirmation. If we divide all Liberals 
into Unionist Liberals and Gladstonian Liberals we can go 
from ' That Liberal is not Unionist ' to 'He is not not 
Gladstonian.' So too in a pure nexus with a negative 
consequent : ' If powder is slow-burning, it does not strain 
the gun unequally.' Under this judgment, if we know that 
the powder is not slow-burning, we are able to say that it 
fails in the quality of not straining the gun unequally. 
We can unquestionably get this inference whenever we 
approach the knowledge of a pure ground. The pure 
ground and the limitation of cases are merely different 
aspects of the same form of knowledge. The ground is 
the fundamental and operative character by which a system 
imposes certain relations on its parts ; the limitation is the 
external and formal consequence of these relations which 
may be mimicked for the purposes of common logic by an 
arbitrary or conventional restriction of alternatives. 

My only difference from Mr. Bradley consists therefore 
in the view which I have maintained throughout, that apart 
from some limitation there is no intelligible negation 
nothing but the infinite judgment, and therefore in strict 
logic no negation at all. Under such a limitation we can 
always go from denial of a positive quality to a positive 
result which we may as a matter of both theory and of fact 
approach from the side of double negation, although of 
course the identity of double negation with affirmation is 
in a reflective stage of culture too immediate to admit of 
the two being really distinguished. The reason for which 
I am anxious to insist on this not very practical distinction 
will appear more clearly when I come to speak of induction. 
It is, in brief, the importance of the negative instance ; 
that is, of approaching any positive content from the side 
of its limit, of the exact boundary at which it ceases and 

Y % 


324 Negation, Opposition, and Conversion, [booki. 

some other content begins. For this boundary is a negation 
by denying which we not only affirm the content that lies 
within it, but affirm it in its conditions and genesis, at 
least for knowledge. ' If a nation has no true art it is 
not religious ' is a judgment that gives the analysis of 
a group of ' negative instances,' which analysis passes into 
an affirmation supported by those instances, in the form 
'A nation which has true art is not not religious.' The 
conclusion thus obtained, ' This nation (having true art) is 
religious ' may be bond fide arrived at through the double 
negation I have described, and may be at first unsupported 
by the direct observation This nation is religious.' 
Conver- iii. Conversion is usually treated with opposition under 

the head of immediate inference. It is primarily a transition 
from one grammatical form to another which introduces no 
new elements into the content. Whether, or in what cases, 
it really involves inference, i.e. a passage from oris judgment 
to another warranted by the first, is the main question 
which arises in treating of it, and of course includes the 
problem what inference, if any, is involved. 

The unity of the judgment, it will be remembered \ does 
not exclude a considerable measure of diversity. It is often 
a mere chance whether a range of affirmative thought is 
condensed into one proposition or comminuted into several. 
And inference is working through the whole of such a range 
as the judgment gains depth and width, and defines its edges. 
Thus, if we mean to say anything definite about the point 
at which we pass from one judgment into ' another,' we must 
look at what is bond fide implied as the essential import of 
the judgment-forms that we discuss, and not at the actual 
transitions which attend our interpretation of any propo- 
sition, and which vary with mental endowment in the 
interpreter, and with the lucidity of expression of the given 
sentence. That is to say, we must distinguish interpretative 
inference from substantial inference transition within the 
judgment from transition between two judgments. 

1 See above, chap. i. 

chap, vii.] Mere Transposition. 325 

The question may seem indeed to settle itself at once. 
The unity of judgment is determined prima facie by the 
unity of the Content judged. A new subject or a new pre- 
dication, i. e. one not related as part within whole to that of 
a given judgment, is needed to constitute another judgment. 
But in immediate inference there is no new content at any 
rate no new positive content. Can there then be a new 

The real interest of Conversion lies in the discussion which 
it provokes of the precise relations imposed upon its content 
by any given judgment, and of the boundaries which sepa- 
rate the bona fide meanings of the various judgment-forms. 
In arriving at these relations or at this meaning we use 
interpretative inference ; it is only when we find ourselves 
able to go from relation to relation by re-applying the 
same form of judgment, or from meaning to meaning by 
passing from a judgment of one type to a judgment of 
another, that we are really employing substantial inference. 
It does not much matter, however, where we elect to draw 
the line of transition from judgment to judgment, so long as 
we understand the connection of the implications concerned. 

a. I will begin with an accidental case of simple con- simple 
version, not recognised in the text-books because the content Conversion 

,....,. . M of Singular. 

of predication in singular judgment is not necessarily of 
singular reference. ' The Duke of Cambridge is Com- 
mander-in-chief.' I think it is beyond question that this 
proposition might be met with ' The Commander-in-chief is 
the Duke of Cambridge ' in a tone which would give it the 
force of a criticism or retort, although its content would be 
warranted true by the proposition as first enunciated. I am 
not prepared to abolish the distinction of subject and predi- 
cate within the judgment, and if we retain the distinction, 
then the mere transposition of the two makes a difference. 
We understand the subject primarily as a designation and 
the predicate primarily as an attribution. The idea of 
concrete individuality clings to the subject, and that of 
specially selected determination' to the predicate. The 

326 Negation, Opposition, and Conversion. [BookI. 

second of the above propositions might certainly be under- 
stood to mean that the qualities of the office were limited 
in the relation in question by those of the individual, and 
not those of the individual adapted to those of the office. 

If it is replied that this may be possible enough, but that 
really one who commits himself to the former proposition 
has bound himself to know and judge the concrete synthesis 
of qualities which the predication constitutes along with its 
subject, I cannot deny that this is so. And I am therefore 
content to rank such inference as is illustrated by the above 
transition under the head of interpretative inference, i.e. 
inference that falls within the logical unity of the judgment 
as bond fide expressed by either propositional form. It is 
true that in some simply convertible judgments, e.g. ' A = 
B in weight,' the order of terms can make no possible 
difference of import. But the reason of this is not that 
the proposition is simply convertible, but that the content 
is of a highly abstract character which annuls all indivi- 
duality, and thus destroys any significance that might attach 
to the difference between subject and predication. A 
similar character belongs in some degree to all quantitative 
Conversion j3. The Universal Affirmative Judgment (under which, in 
tion imlta ordinary logic-books, the Singular Judgment is compre- 
hended) is not admitted to be convertible simply, i. e. by 
mere transposition of subject and predicate, but is sup- 
posed to be convertible ' by limitation/ i. e. by trans- 
position together with reduction to the level of a ' particular ' 

With reference to the first part of this rule, the whole 
course of our investigation of judgment is a comment on the 
degree and rationale of its truth. It is equally certain that 
the prohibition of simple conversion is warranted by common 
usage, and that the ' pure case ' (which does not mean mere 
tautology) is an ideal operative throughout the judging 
activity. I am confident that Quantification of the Predicate 
and the Equational Logic owe much of their success to their 

chap, vii.] Conversion of Generic Judgment. 327 

recognition of this ideal, though their forcing it upon the 
ordinary judgment by truncating the meaning of the latter 
is a blundering anticipatio naturae. 

The second part of the above rule, the ' limitation ' of the 
converse, has different values as applied to different classes 
of judgment which correspond to the so-called 'universal 
affirmative.' If we take a judgment of the collective type 
and argue e. g. that because ' All houses in this street have 
gardens ' therefore ' Some houses which have gardens are in 
this street' we do not seem to gain anything by the 
re-arrangement. And we certainly lose something, for we 
cannot recover the original judgment by re-conversion of 
the particular thus obtained. Of course re-conversion can 
only give ' Some houses in the street have gardens.' But 
we know, to begin with, that all the individual houses in the 
street unite with their other attributes that of having 
gardens. We seem, then, only to have advanced to a doubt 
of what we knew. There is however a shade of difference 
suggested, as in the singular judgment examined above, by 
the mere transposition of subject and predicate. The de- 
nomination of the individuals is less emphasised than the 
content enunciated of it. The former fills the place of 
pointing with the finger to an object of perception, the 
latter that of the significant ideas by which the perceptive 
judgment qualifies such an object. But this transition 
seems to fall within the interpretative inference, and not to 
amount to substantive inference. 

In the case of the generic judgment of either type the 
import of the change becomes more emphatic. ' The 
dahlia is one of the Compositae ' tells me that this regular 
flower, apparently a mass of petals like a garden rose or 
peony or hollyhock, is really an aggregate of little florets 
like those of the daisy or dandelion K In short, this judg- 
ment distinguishes the dahlia from flowers externally not 

1 In the double dahlia the form till lately commonest in gardens every 
floret is developed into a one-sided corolla like those of the florets which form 
the ray of the common daisy. 

328 Negation, Opposition, and Conversion, [booki. 

unlike it, but having no structural affinity with it whatever. 
' The Compositae include the dahlia,' or * Some Compositae 
are dahlias,' presents us with the typical or generalised 
structure of a Composite flower determined and differenti- 
ated by the peculiarities of a dahlia. The rose or peony 
would in this case never come into our heads ; we should 
be occupied with some such individual as the daisy or the 
thistle, and the object of the judgment would practically be 
to distinguish the dahlia from other Compositae, not to 
distinguish it from flowers which are in no way akin to it. 
The one judgment qualifies the external appearance of a 
dahlia by the internal structure of the Compositae ; the 
other qualifies the diagrammatic type of a composite plant, 
as admitting, among others, of the specific peculiarities of 
the dahlia. 

I have but little doubt that this account represents 
the meaning of the two propositions in fact. But it may 
be said that we have no right to separate them, and that 
we ought to demand the explicit recognition of both 
these determinate affinities as essential to the meaning of 
the generic universal judgment itself ; and it may even be 
insisted that if the second proposition contains more than 
the first in any respect e. g. in the more concrete appre- 
ciation of diversities of composite structure then it cannot 
be warranted by the first. This latter suggestion would 
make short work of all conversion whatever beyond the 
rank of grammatical change, unless ttXzov rjfiLav ttclvtos 
mere selection can make the old into new, or unless some 
principle is appealed to that goes beyond the judgment 
itself. The former part of the objection may be met by 
saying that undoubtedly the original judgment may be 
made with the whole significance of the two propositions ; 
but that when so made it is somewhat artificial, and that 
the distinction of a specific adaptation within the Composite 
type is naturally a different process from the qualification 
of a given shape by the abstraction of that type. I may 
put the antithesis thus: the generic judgment, which we 

chap, vii.] Modal Conversion. 329 

took as the convertend^ if completed into identity, would 
determine the composite type by limitations restricting it to 
the case of the dahlia ; while the particular, in this case the 
converse^ if similarly completed, would extend the range of 
species by disjunctive enumeration till they expressed the 
whole content of the natural order of Compositae. 

y. This conversion of a generic judgment may be taken Modal 
either as interpretative or as substantial Inference. Tested s in Ver ~ 
by common usage it is, I incline to think, a substantial 
transformation, resting on some such- principle as the 
possibility of treating every content in turn as quasi-indi- 
vidual. Tested by the logical ideal, it is a mere phase 
in the interpretation of the judgment, which involves re- 
ciprocal determination in the affirmation of a nexus. In 
either case it contains the only fundamental principle on 
which conversion can really proceed ; viz. that every con- V 

tent can be exhibited as a quasi-individual element in a 
system. This is, for instance, the principle of which ' modal ' 
conversion is merely a corollary. In the typical example 
employed above modality has no real application ; modality 
only appears where the disjunction is one of ignorance. 
The particular judgment ' The type of the Compositae in- 
cludes among its alternative modifications that of the 
dahlia ' may be read into ' A composite may be a dahlia,' 
i. e. the fundamental structure C is a real element compa- 
tible with the modification D. But this is a mere conse- 
quence of feigning ignorance when we have knowledge ; 
in order to get the possibility we have to imagine that 
conditions are unknown which in fact are distinctly known 
and enter into the content of the judgment. 

The pure Hypothetical Judgment differs from the Generic 
by disregarding individuality, and therefore the above prin- 
ciple is disguised in converting a Hypothetical, so that we 
appear in this case to obtain pure modal conversion. ' If 
arsenic is taken in such and such a quantity, it will cause 
death with such and such symptoms,' which gives the con- 
verse ' Death with such and such symptoms at least may 

330 Negation, Opposition, and Conversion, [booki. 

have been caused by arsenic.' This is a motived possibility 
I or real possibility, not a mere possibility, and forms a sub- 

stantial conclusion and one warranted by the convertend. 
But this result is still rather a corollary from the converse, 
than the converse itself. The example just quoted is one 
hardly deserving hypothetical form. It involves no trace- 
able modification such as to set up a clear nexus between 
antecedent and consequence. Thus we cannot assign any 
precise conditions under which the consequent is related to 
the given antecedent, and the possibility that such death 
may result from such poison is merely a fact plus unknown 
alternatives. In a true hypothetical there is more than 
this. Grant that it is not simply convertible, still we can 
bring the possibility home to the nature of the consequent. 
1 If straight lines are parallel, they do not tend to meet.' 
The real converse of this is, 'Straight lines in the same 
plane which do not tend to meet are parallel.' But the 
limiting condition is not given in the convertend. Nor 
do I mean that we have a right actually to state it in the 
converse, but yet we must think of the converse where 
such a condition can be suggested as exhibiting a real if 
undefined attribute of the content which is now the subject, 
in virtue of which this content includes the case mentioned 
in the antecedent of the convertend. The affinity between 
generic judgments and the more valuable hypotheticals is 
very close, and we lose all hold on the generic element in 
\j judgment if we insist on reducing a definitely determinable 
content to one real alternative in an unknown number of 
unknown ones. I cordially agree therefore with Mr. Bradley's 
distinction between real and mere possibility, and only in- 
sist that the true content even of a modal converse is the 
positive nature in virtue of which the subject-content is 
variously determinable, and not a mere conjunction of 
attributes plus other unknown conjunctions. 
Simple g. We are now to speak shortly of conversion in which 

ofUniver- the negative is employed. Every negation rests, as we 
sal Nega- have seen, in its purely formal aspect, on the ultimate or 

Chap, vii.] Elementary meaning of 'Negation. 331 

absolute disjunction. But it does not follow from this 
that a real process of substantial inference takes place 
where negation intervenes. 

I begin with the simple conversion : ' A is not B,' there- 
fore ' B is not A ;' ' No negroes have straight hair,' ' No 
straight-haired man is a negro.' I should certainly prefer 
representing this transition as a true process of argument 
to illustrating it by a diagram of two separate circles, be- 
cause by the latter means we destroy all idea of the struc- 
ture of the judgment. But yet I cannot think that in our 
present stage of reflection the argument if any is more 
than interpretative, i. e. more than we are always using in 
arriving at the full meaning of any sentence. We can 
formally trace out the process of inference, but in using 
it we are like an engine running free and doing no work. 
No doubt the formal steps are, beginning from the ulti- 
mate disjunction between 'is' and 'is not,' to say 'No 
negroes have straight hair;' ' Straight-haired men are either 
negroes or not ;' ' If negroes, then they are both straight- 
haired and not straight-haired ;' ' Therefore it is false that 
they are negroes,' ' therefore they are not negroes.' But 
all this is given in the meaning and practice of any civilised 
language ; and though it might be possible to stumble in 
using this converse *, that is no more than may happen 
in reading any sentence however simple. The elementary 
meaning is simply that the two contents are in the relation 
of abstract otherness to each other, and refuse to be brought 
together in the modified or concrete otherness which sub- 
sists within the affirmative judgment. 

e. Contraposition seems to contain a more remote con- Contra- 
clusion. It goes from A is B, to Not-B is not A, e.g. from P osition - 
' Every negro has woolly hair ' to ' A man who has not 
woolly hair is not a negro.' I remark on this process, i. 
that the skeleton argument with symbolic letters seems 
far more remote and obscure than the intelligible example ; 

1 As e.g. if any one tried to argue that 'All not-straight-haired are 

332 Negation, Opposition, and Conversion, [booki. 


tion and 

ii. that we are much hampered in the apprehension of our 
inference by being forbidden to conclude that 'Not- A is 
not-B,' which the ideal of judgment demands as the ex- 
pression of the negative instance, ' Just not- A is just not-B,' 
e.g. the affirmative being 'True freedom is virtue' 'If 
you fail to produce freedom, you fail so far and for that 
reason to produce virtue.' And, iii. substantial inference 
is less likely here, for the unity of the judgment is 
much greater in affirmation than in negation ; and when 
we have just, so to speak, dipped the object a in the 
colour b, it seems idle to ask on the basis of that judgment 
whether what is not of the colour b can be the object a. 
We are in fact no longer dealing with a and b, but with a b 
as including all a. We may say of course, ' Oh yes ! not- 
is not-tf, because if not-# is a then it is b! But this remark 
is made ready to our hand ; we have just qualified a by b 
and therefore are at least entitled to ' a is not not-#,' which 
brings back our problem to the last head, that of simple 

In short, then, in both these cases we employ the absolute 
alternative ; but this is given in the form of negation or con- 
tradiction, and needing no true limitation of alternatives, 
can only rank as a formal principle of intelligible thought 
and speech, not as a real addition to content of inference. 
Transition by help of such a formal principle I call Inter- 
pretative Inference. 

5. The external shape of negation belongs as we saw to 
ignorance, and significant negation is knowledge disguised 
as ignorance. For bare denial would be devoid of meaning. 
Now this external shape of negation seems really appro- 
priate where positive knowledge fails, i. e. in the region of 
what has been called Privation \ the mere absence of 

1 ' Privation,' Privatio, used by Sigwart as equivalent to Aristotle's areprjais, 
OTeprjTitcos, and as contrasted with opposition, kvavTLorrjs, and distinct from 
negation, dirocpaais. ^reprjais seems to be applied to any negative enunciation, 
airocpaais only to the denial of an affirmation ; see Aristotle's Organon, 38 b, 1 3, 
with Waitz's note. Unluckily the distinction of privative and negative terms 
as given e. g. in Whately's Logic has just the reverse meaning to that of 

chap, vil] Does not-impossible = possible f 333 

positive determination. But this region is also the region 
within which there falls the limitation of knowledge, a 
matter of the most serious and positive import. Where 
knowledge simply fails us, and consequently we seem to 
have nothing left but privation or bare denial, how are 
we to pronounce on any suggested possibility, a. by way 
of affirmation, /3. by way of exclusion ? 

The case a is the more complicated of the two. The Privation 
privation or bare denial is in this case the bare denial of p^sibiHty 
an incompatibility with reality, i. e. of an impossibility. 
Exclusion, as we have seen, must rest on a positive quality, 
a ground of negation. Here, ex hypothesis we can find no 
exclusion of the impossibility. We are supposed to know 
simply nothing, either pro or con, about the positive matter 
whose possibility is in question. Are we therefore bound 
to admit that it is not not-possible, and, as a consequence 
of this double negation, that it is possible ? If we are led 
to do this and the trick is often attempted, especially in 
popular theology we feel that we have been cheated. A 
possibility, in the usual sense of the term, is something. 
We are foolish if we do not keep it in view and let it in- 
fluence our deliberations in any way which its nature de- 
mands. Yet this something has here ex hypothesi been 
created out of nothing. But in knowledge at least nothing 
can come of nothing, and we are trapped in a contradiction. 

What we have to remember is that our denial of the 
exclusion of the positive content is or approximates * to a 
bare denial ; or in other words, rests upon no positive 
ground. We do not exclude the impossibility; we only 
fail to find it. And therefore our denial is meaningless 
or nearly meaningless, and amounts to nothing. In other 

privation and negation in Sigwart and Bradley. ' Privative ' in "Whately indi- 
cates a positive opposite, and 'negative' a mere absence. The association 
with active ' deprivation * implying a loss appears to be the cause of this usage. 
1 ' Approximates ' for a suggestion, if intelligible, contains some ground in 
its mere conceivability, and thus affords material for intelligible support or refu- 
tation. But by far the larger element in the importunity of many suggestions is 
drawn from the fallacy of inferring from non-impossibility to real possibility. 

334 Negation, Opposition, and Conversion. [booki. 

words, the possibility which we are asked to infer from 
mere not-impossibility has as so inferred no foundation in 
positive reality. A real possibility of any result consists in 
something given as actual, which, under conditions of 
known nature and not known to be impossible, would give 
that result. A gun forms a real possibility of shooting, if 
there is no reason to suppose that cartridges are not to be 
had ; an acorn is a real possibility of an oak, if we know of 
nothing to hinder its being planted and growing. But in 
the case supposed we have nothing like this ; we have 
simply nothing a failure to find incompatibility. There- 
fore we ought, strictly speaking, to conclude not that it is 
possible, which is an affirmation, nor even that it is not im- 
possible, which borrows the form of intelligible denial, and 
therefore presupposes a positive ground of denial, but 
simply that we do not know it to be possible. This con- 
clusion gives its true value to the form of bare denial by 
making the ground of negation what in the case of ignor- 
ance it really is, an actual state of our own minds which 
excludes the knowledge in question. 

Instances of assertion resting mainly on this confusion 
are to be found e. g. in expositions of the so-called modern 
Buddhism, the elaborate dogmatic fabric of which is chiefly 
protected from criticism by the impossibility of discovering 
any ground on which it may be taken to rest, and against 
which, therefore, a positive objection can be raised. 

To put the point in other words, in the case before us it 
is not true that double negation is equivalent to affirmation. 
For the double negation in question is founded neither on 
the affirmation itself, nor on the denial of a specific alterna- 
tive to the affirmation. If there were such a specific 
alternative to the affirmation, it could only be denied on 
some positive ground, and such a denial would not be the 
bare denial of which ex hypo the si we are treating. 

Or again, without appealing to the difference between 
privation, i. e. bare denial, and exclusion a confusion be- 
tween which processes however is the root of the fallacy 

chap, vii.] Privation and Exclusion. 335 

we may simply lay it down that a real possibility is 
something actual, and that a bare denial affirms nothing as 
actual, and therefore a bare denial cannot affirm a real 

And it must be added with reference to remote sugges- 
tions generally, that a failure to demonstrate impossibility 
can almost always be secured by a high degree of remote- 
ness or of abstractness in the suggestion itself. Thus, if 
accepted as really possible because not demonstrably im- 
possible, such a suggestion would profit by its own wrong. 
Reality cannot, for us, contradict a suggestion that has no 
point of contact with reality. Things in themselves, 
according to the popular notion of the Kantian doctrine, 
are the content of such a suggestion. They made no claim 
to affect knowable Reality, and therefore knowable Reality 
can present no quality which excludes them. As a rule, to 
disprove the grounds on which a fact is advanced is not the 
same thing as disproving the alleged fact ; denying the 
antecedent does not amount to denying the consequent. 
But in the case of unverifiable suggestions the grounds 
which are implied in the suggestion are for a given state of 
knowledge the sole grounds conceivable, or at least the 
grounds which can be stated are capable of exhaustion, 
and the disproof of them may be taken as for that state 
of knowledge disproving the suggestion. It must be 
remembered that denying the antecedent does deny the 
consequent qua consequent of the antecedent denied. At 
any rate it is clear that in such cases as those under dis- 
cussion the failure to prove impossibility which arises 
from the emptiness of the suggestions themselves must not 
be taken as amounting to the establishment of real pos- 

. We cannot go from bare denial, or privation, of an Privation 
impossibility, to real possibility, because privation of im- sibiiity P S 
possibility does not involve positive affirmation as the 
exclusion of impossibility does. It may seem therefore 
that we have decided in the negative by anticipation the 

32>6 Negation, Opposition, and Conversion, [booki. 

question whether privation or bare denial can ever justify 
exclusion. We denied the claim of privation to establish 
real possibility, on the ground that it could not exclude, 
as one form of the ground that it could not affirm. Thus 
when we omit the incompatibility or impossibility, and 
consider merely the exclusion of any positive content, it 
seems that we cannot predicate exclusion on the strength 
of privation. Up to a certain point common sense and 
experience support this result. Gold has never been found 
in Northumberland, but that alone does not prove that it 
never can be found there, unless the geological formation 
forbids, i. e. is a positive ground of exclusion. 

Still, the two transitions, from privation of impossibility 
to affirmation of real possibility, and from privation of 
actuality to exclusion of possibility or of actuality, do not 
stand on quite the same level. The former is explicitly 
a passage from denial to affirmation, or, as we saw, from 
nothing to something. The latter retains its negative 
form and vehicle unchanged, and leaves the change of its 
ground and bearing, the two other elements of meaning \ 
to be moulded by the context. Any mere denial or priva- 
tion when expressed intelligibly is given a ground and 
bearing with reference to our cognitive state, as we saw in 
dealing with the instance, ' We do not know that there are 
things in themselves/ What is a bare denial with reference 
to reality is a positive affirmation about our knowledge. 
We have agreed that we cannot transform 'We do not 
know it to be impossible ' into ' It is possible.' Can 
we transform ' We do not know it to exist ' into ' It does 
not exist ' ? 

It is plain, I think, that many beliefs become abortive 
and cease to be regarded because we become convinced 
that reality does not constrain us to accept them. And it 
seems an unworthy shirking of a theoretical difficulty to 
treat these beliefs as shelved but not denied. If, whether 
in serious speculation or in grave practical deliberation, 
1 See above, p. 305. 

chap, vii.] Doubt involves Knowledge. 337 

some idea cognate with the matters then before the mind 
has ceased to exercise the slightest bias on thought or on 
action, it seems idle to say that upon such an idea we have 
suspended judgment as upon something that may be true 
in itself but is nothing for us. It seems clear that upon 
such an idea I may instance the Swedenborgian hierarchy 
of spiritual beings we have in fact sate in judgment and 
have condemned it as unreal. But I admit that the specu- 
lative expression of our relation to such conceptions meets 
with serious difficulty from the necessity of basing denial 
upon a positive ground. On what positive ground can I 
base a denial that there are exactly seven heavens, or 
that there are just seven orders of superior spirits? I un- 
questionably do deny it, that is to say, ' I do not believe it.' 
The habitual use of such phrases as this 1 , which refer 
grammatically to a fact of my intellectual state, but actually 
serve as negations of something ascribed to reality, bears 
witness to the connection which I am attempting to 
point out. 

Incompatibility in the ordinary sense depends on the 
system of reality. Differents which claim the same place 
are incompatible, and, in short, everything is incompatible 
with reality which, while not conforming to our ideal system 
which stands for reality, is yet without the power to modify 
it. But, as I pointed out above, all this falls to the ground 
where the system does not extend. Where ' we do not 
know' in the sense of having no knowledge not merely 
in the sense of lacking complete knowledge we can say 
nothing, and ex nihilo nil. * Then,' it may be said, ' neither 
acceptance nor rejection? I cannot follow this. Know- 
ledge is positive, and acceptance and rejection are not co- 
ordinate alternatives. We doubt, where we have a basis 
of fact to go upon, and presumptions that appeal to that 
basis ; but where we have nothing to go upon we cannct 

1 Compare ov Qrjfii, which means 'I deny,' or our common phrase 'I don't 
think that 'which is really equivalent to ' I think that not.' 
VOL. I. Z 

338 Negation, Opposition, and Conversion. [Booki. 

The only conclusion that I see open to us is of this 
nature. Where privation seems to warrant exclusion, we 
must look for the positive ground of exclusion in the deter- 
minate completeness of our ideal Reality. Such a ground 
may be hard to state, and may amount in positive content 
to little more than our experience of the persistency of the 
privation. But its nature must be that the ideal Reality 
by its organised completeness excludes the matter which 
attempts to introduce itself. This must not be taken to 
mean that we are nearly omniscient. It means that the 
general plan and growth of our knowledge is such as to 
afford no basis of attachment for the proposed accretion, 
although for this very reason we are unable to specify any 
definite antagonism between the content suggested and the 
positive contents already accepted as part of Reality. 
Reality is not especially incompatible with seven heavens ; 
it could be so only if we accepted some kind of heaven as a 
reality and were prepared, on the basis of our knowledge 
about it, to reject either the particular number seven, or the 
application of number to such a subject at all. What we 
really have to say is that we do seem able to trace, however 
imperfectly, something like a development of the sensuous 
into the spiritual world ; and that the main lines of this 
development appear to have a completeness of their own, 
without growing out into a duplicate and quasi-material 

It is not enough to destroy the grounds on which a 
suggestion is explicitly based, unless we can show that they 
form not merely the sole ground alleged, but the sole 
ground possible. And in a region beyond our knowledge 
this ex hypothesi cannot be done. It is often possible to 
show by what logical fallacy or by what psychological 
tendency a suggestion was generated ; but this is not a 
logical refutation. It may however grow into a refutation 
if, besides the tendency which caused the error, we can 
exhibit the satisfaction which reality offers to the rational 
necessity embodied in that tendency. We thus not only 

chap, vii.] General and special Negation. 339 

destroy the raison d'etre of the error, but show a presumption 
that there is an excluding ground. 

Exclusion by Privation then rests on a conviction, won 
by persistent lack of affirmation, of the true negative limit 
and external contour of knowledge, which limit, qua the true 
limit, must be held true of reality. A privation cannot 
ultimately be referred to our knowledge only. If persistent 
in the history of thought and justified by the tendencies of 
knowledge, it must sooner or later be taken as true of 

At best, we must remember, negation is always negative. 
The last step from the positive ground to its formal expres- 
sion by means of denial, retains the form of privation, i.e. of 
ignorance. This is what the old saying means, ' you cannot 
prove a negative.' The negation is not after all quite the 
same as the positive opposite latent under the negation. 
You cannot prove that parallels never meet. In order to do 
so, you would have, like the Irishman, to ' be there when it 
did not happen.' You can only prove that they always do 
this, that, or the other which in virtue of your geometrical 
experience you take as equivalent to not meeting. That is 
to say, assuming your geometrical system to be ad hoc 
exhaustive, then your failure to see, on the basis of that 
system, how parallels can meet becomes knowledge though 
it retains the form of ignorance. It expresses a limit or 
outline essential to geometrical science. Thus the cases of 
persistent privation and of true positive exclusion (genuine 
denial, not bare denial) differ simply by the nature of the 
positive ground which underlies them respectively. In 
privation this ground is general, drawn from the character 
and tendencies of Reality; in true exclusion it is special, 
drawn from a system within which the alleged reality would 
fall. It would seem fair to concede to the former somewhat 
more and to the latter somewhat less finality than common 
theory recognises. 

Z 2 


Disjunction and the statement of Chances. 

The pis- i. The Disjunctive Judgment combines in an explicit 
judgment, form the characteristics of the Generic and of the pure 

Hypothetical Judgments, 
its Genesis, i. It is needless however, and would be artificial, to 
lay down rules for the precise mode of transition from 
these judgments to the complete Disjunction. The whole 
assertory state within which the simpler forms of judg- 
ment, at any rate from Comparison upwards, have their 
import, is from the first of a disjunctive nature. Re- 
flection may therefore be stimulated to the explicit 
formulation of this type of knowledge by very various 
^ occasions. But the common ground which must operate in 
all these occasions is the discovery of differences into each 
of which the identity underlying all of them enters as a 
whole, and in all of which taken together its manifestations 
are exhausted. Every difference has the former of these 
characters in some point of view. A conjunctive judgment, 
or conjunction of judgments with an identical subject, can 
always be made disjunctive by wilful abstraction. A 
diamond is carbon, and crystalline, and very hard, and 
highly refractive. This is a conjunctive judgment or set of 
judgments 1 . But if we limit the underlying identity, the 
nature of the stone, by the several conditions under which 
it exhibits these several predicates, then each of these 
predicates may be regarded as not conjoined with but 
exclusive of the other attributes enumerated. A diamond 
may be considered either merely as an element, or merely 
as a transparent substance exhibiting crystalline structure, 
or in its power of scratching other hard substances, or in its 

* * See above, chap, i, on the Judgment in Time. 

Transition to Disjunction. 341 

effect upon light. This is disjunction arbitrary and sub- 
jective, if we please, but still disjunction. Any distinguish- 
able attributes may be regarded as reciprocally exclusive by 
our simply refusing to attend to more than one of them at 
once, x may be both a and b, but qua a it is not b. But 
in another respect also the above instance of disjunction is 
bad and arbitrary. It makes no serious attempt to exhaust 
the attributes. We stop enumerating them simply because 
we do not care to go on. 

It is clear that a disjunctive judgment may originate with 
a conjunction of judgments like the above, which turn out to 
have assignable relations to one another, or, again, with the 
discovery of an error in a generic judgment; e.g. ( Cereus 
is a night-flowering plant.' ' No : Ceretis grandiflorus is a 
night-flowering plant, but there are a hundred species of 
Cereus^ and not all are night-flowering.' Such considera- 
tions would force upon us the disjunction, ' Cereus blossoms 
either at night, or in the early morning, or etc., etc' Again, 
the attempt to convert a generic judgment naturally leads to 
a disjunction l . And so does the challenge thrown down by 
the specific condition and consequent of a pure hypothetical 
judgment. ' If we catch the train this morning we reach 
London to-night.' In presence of such an assertion it is 
not in human nature to abstain from asking, 'And if we 
miss the train, what then?' so as to make explicit the 
disjunction, 'We either catch the train or miss it;' and 
probably some such further consequence as, ' We either get 
to London to-night, or have to sleep at Crewe.' 

All these are merely different ways of giving utterance to 
the interest which attaches to some pervading identity and 
compels us to pursue it throughout its modifications. Such 
an interest, as we have seen, environs every genuine judgment, 
and makes it an element in a system. And in proportion 
as such a system is made explicit, negation enters into 
knowledge. For in every system the parts have an aspect 
of negative relation to one another. 

1 See above, chap, vii, on the Conversion of generic judgments. 



342 Disjunction and the statement of Chances, [book i. 

Thus the immediate occasion on which we form a disjunc- 
tive judgment may vary. But the characteristics of true 
disjunction do not vary. By true disjunction I mean a 
judgment in which alternatives falling under a single identity 
are enumerated, and are known in virtue of some pervading 
principle to be reciprocally exclusive, and to be exhaustive. 
This is the disjunction of which I shall treat, being convinced 
that what seem to be different kinds of it are in fact nothing 
but imperfect examples. 

ii. I will mention three of these. 

a. First, there is the so-called disjunction in which the 
alternatives are exhaustively enumerated, but are not taken 
to exclude one another. ' He is either knave or fool ' 
does not, it is said, exclude the possibility that he may be 
both. On the question of the genuineness of these dis- 
junctions I must refer to Mr. Bradley's detailed discussion 1 , 
which appears to me to show decisively that we never 
really mean to take into consideration under our judgment 
the conjunction of the alternatives specified in our ' Either ' 
' or.' Without following him into the study of grammatical 
details, I content myself with remarking that any Disjunc- 
tion in which the alternatives are not reciprocally exclusive 
must of necessity fail to be exhaustive the case or cases 
in which any of them are conjoined being casus ornissi* 
If, for the purpose of the disjunction, such a case may be 
reckoned under one of the other alternatives, then indeed 
the disjunction may be reckoned to be perfect; but then 
the case of conjunction does not rank as conjunction, but 
under one or other of its component elements. Thus, ' To go 
by train you must have either a first, second, or third class 
ticket.' A man may of course buy all three, if he pleases ; 
but the possession of them does not constitute a fourth case 
of liberty to go by the train. He goes by the train in 
virtue of one or other, though he may change carriages at 
every station if it amuses him. The conjunction of all 

1 Principles of Logic, Book I. chap. iv. 

chap, viii.] Ignorance on a specific point. 343 

three tickets forms no separate alternative as a particular 
way of going by train, and therefore is rightly disregarded 
in the disjunction. It is not indeed implied that ' If he has 
a first-class ticket he has not a second or third,' but it is 
implied that * If he goes in virtue of a first-class ticket he 
does not go in virtue of a second or third.' 

/3. Secondly, there are the troublesome cases often taken Disjunc- 
as the true instances of Disjunction, which may be called ignorance. 
1 Disjunctions of ignorance.' The essence of these is that 
they refer to an individual (actual or supposed) and not to 
an individuality, and consequently express doubt or indeci- 
sion rather than knowledge. 

* A triangle is either isosceles, scalene, or equilateral.' 
A triangle here can mean any individual triangle you may 
pitch upon 'any given triangle.' And with respect to 
such an individual triangle the disjunction says that it 
must belong to one of the three kinds mentioned, but 
that we do not know to which. Lotze, for instance, V 

appears to accept this expression of indecision as the 
final type of disjunction. But it seems obvious that 
this uncertainty is purely dramatic or fictitious, and is a 
mere corollary from the true disjunction, which is, ' A three- 
sided plane figure as such must have all its sides equal, or 
two only equal, or all unequal.' Or we may take a case 
where the doubt is real, as often in common life; but 
here also it is a mere application of or inference from the 
true disjunction of knowledge. ' Being an Oxford man, he 
is either a University College man or a Balliol man, or 
etc.' This judgment, which is a real expression of doubt or 
ignorance, is based of course on the positive knowledge that 
the conditions of University life require the student as such 
(generically) to attach himself to some one of the corporate 
bodies enumerated in the judgment. With disjunctions of 
this type we must class the commonest of all expressions 
of doubt or ignorance. ' He is either angry or jealous,' 
' He has either measles or scarlet fever. 5 These, like the 
above, differ not in principle but only in perfection from the 

344 Disjunction and the statement of Chances, [booki. 

ideal disjunction. What operates is something we know, 
and know to contain the specified alternatives. We do not 
however specify our knowledge in detail it may consist in a 
content hard to define and we merely point to the concrete 
individual, in whom it is embodied and from whom it takes 
its interest. About this individual, as his complete state 
goes beyond our knowledge, the judgment takes the shape 
of doubt, just as in the case of ' any given triangle.' The 
higher logical form may be imposed on the lower content ; 
this is a possibility which follows from the nature of reason, 
and which makes abstract distinction appear in some aspects 
\ so valueless. Every thinkable content has in miniature all 

the characteristics of reason, and in the abstract you can 
hardly say anything of the self-conscious mind which is not 
also true of a protococcus or of a pebble. The precise 
modes and degrees in which the content fulfils the spirit of 
its abstract form are what we must keep our eyes on in a 
true concrete science. I cannot admit then that the mere 
inference from our disjunctive knowledge respecting that 
which an individuality implies, to a doubt respecting a 
given or supposed individual, has a claim to rank as a 
genuine species of disjunction. 
Disjunc- y. it is a similar vice to account for the exclusiveness of 

tions re- -. . . _ . - . __ . 4 

ferred to disjunction by referring it to a point of time. No judg- 
Em? f ment whatever refers to an atomic point of time ; and no 
universal judgment refers to any time except that implied 
in the content of the judgment itself. The time at which 
the predication happens to be made has nothing to do with 
the import of any judgment except in as far as it is taken 
into the content by reference direct or indirect to present 
perception 1 . The denial of coexistence in time, which 
appears in some disjunctions to be the principal meaning, is 
a corollary from the nature of the disjoined contents, not a 
result of the present tense employed as a vehicle of pre- 
dication. ' A railway signal shows to the same side either 

1 See above, chap, v, on Time in singular judgments. 


chap, viii.] The Disjunctive Predication. 345 

a red, or a green, or a white light.' Now of course this 
judgment informs us that at any given moment of time 
we shall only see one of the three lights. But to interpret 
the judgment as if it essentially referred either to the 
moment at which it is made or to ' any given moment ' is 
a fallacy on all-fours with that pointed out above of inter- 
preting ' The triangle as = ' any given triangle.' The 
judgment means that the nature of a railway signal is to 
show one light to the exclusion of another and the other to 
the exclusion of the one. From the nature of the case they 
exclude one another in time and in spatial direction. But 
the present of predication is coextensive, in its reference, 
with the nature of the signal, and does not refer especially 
or exclusively to the moment at which the judgment 
happens to be pronounced, nor even hypothetically to ' any 
given moment.' 

We must clear out of the way. then, the above disjunctions 
of ignorance, or dramatic disjunctions, and consider exclu- 
sively the perfect disjunction as a form of knowledge. One 
more peculiar type, indeed, will come before us later as the 
statement of chances. 

iii. A true or ideal disjunction is a generic judgment Logical 
whose content is developed or inter- related by the aid of ftrueDis- 
hypotheticals. junction. 

a. It is a generic judgment because it deals with an The 
individuality, a content which is a whole or system in judgment 
itself. So far, like the generic judgment, it is quasi- 
categorical. The subject is such as can be real, and the 
judgment assumes its reality. But the predication made 
of this real and quasi-individual subject is peculiar, and has 
points of analogy both with the negative and with the pure 
hypothetical judgment. The individuality is exhibited in V 
the different forms which it is capable of assuming as a 
whole, and which consequently it cannot unite in itself 
under a single set of conditions. If the individuality is 
considered as essentially affected by time, these forms may 
be successive ; if it is a generic or specific character, they 

346 Disjunction and the statement of Chances, [booki. 

may coexist in space and time with each other ; all that is 
necessary is that the subject-content should enter as a 
whole into each of the enumerated forms. What, then, is 
directly predicated of the subject-content? I see no 
theoretical reason to deny that the ' either or ' considered 
as the articulate analysis of a universal 1 system of attri- 
butes can be intelligibly and categorically predicated of it. 
Every predication includes differences, and an extended 
present, and therefore predicates as facts elements which 
can be regarded as reciprocally exclusive. In fact, every 
universal is a synthesis of such elements. But undoubtedly 
there will always be positive qualities which are the con- 
densed or summarised expression of the total analysis, and 
may present themselves as its ground, being thus in dis- 
junction as the positive ground or bearing in negation, and 
as the underlying quality in the hypothetical judgment. 
' The triangle is either scalene, isosceles, or equilateral ' 
contains as this condensed relation, or synthesis of differ- 
ences, ' a plane figure bounded by three sides, which may 
have any relative length so long as any two of them are 
together greater than the third.' Such an attribute might 
be called the categorical or positive basis of the disjunction ; 
but it is an illusion to suppose that a basis or ground is 
necessarily more real or more primary than its conse- 
quences, and that therefore the implied predication in dis- 
junction is more categorical than the explicit ' either or.' 
The ground is to its consequences as whole to part ; but if 
the consequences are fully stated in a connected system 
this distinction falls away, and in disjunction such full 
statement is the ideal. 

The disjunction is therefore the only judgment-fon 
that in strict theory can stand alone. All connection is 
within a system ; and only that judgment is self-sufficing 
which affirms at once the system and the connections 
within it. I do not say that every disjunction is thus 

1 ' Universal ' not in the sense of abstract or generalised, but in the sense of 
a concrete identity containing differences. 

chap, viii.] Reciprocal Relations. 347 

ultimately self-dependent, but relatively to a number 
of hypotheticals which have their truth within it every 
true disjunction has a substantive character. Thus the 
disjunction which. lays down the nature and kinds of the 
triangle contains the ground and basis of all the hypo- 
thetical judgments which expound the properties of that 
figure. In other words, if completed and made explicit, 
any one of those hypotheticals would result in that dis- 
junction; which however itself falls within the ultimate 
judgment that would expound the nature and modes of 
space. The above then is the generic or substantive 
element in disjunction. 

j3. But we need in addition the reciprocal relations The Hypo- 
between the forms which constitute the explicit development judgment. 
of this predicated universal. For these relations we must 
go to the hypothetical judgment, and to the hypothetical 
in a very late and artificial form, viz. that in which the 
negation of one content is known as the ground of the 
affirmation of another content, and the affirmation of the 
one content is known as the ground of the negation of the 
other content. The perception of the relations which these 
two types of hypothetical judgment embody is essential to 
the exhaustiveness of the disjunction and to the reciprocal 
exclusiveness of its members. In order to know that the 
alternatives enumerated are reciprocally exclusive, we must 
be able to say (using as an illustration the simplest case in 
which there are only the two alternatives B and C), ' If A 
is B, it is not C And in order to be sure that no possible 
alternative is omitted we must be able to say (in the same 
example) that ' if A is not B, it is C According to a rule 
of Conversion, or rather of Inference, accepted for the case 
of Hypothetical Judgments ('Deny the consequent') the 
equivalent or converse judgments, ' If A is C it is not 
B ' and 'if A is not C it is B ' are involved in the two 
corresponding judgments above mentioned. If this Conver- 
sion or Inference is disputed, then we must say that all four 
cases, ' If A is B ,' ' If A is C ,' < If A is not B ,' If A 

348 Disjunction and the statement of Chances, [booki. 

is not C ,' must be perceived independently before the 
predication of disjoined alternatives is justifiable 1 . 

1 I insert here some details which are legitimate matter of curiosity, but 
would needlessly overload the text. 

i. It might be urged, on the analogy of the argument employed above (p. 342) 
that a disjunction which is thoroughly exhaustive cannot but have its members 
reciprocally exclusive that the hypothetical which prima facie secures ex- 
haustiveness (If A is not B it is C) ought to affirm the reciprocal exclusiveness 
of the antecedent and consequent, i. e. to exclude the case B C. If it did so, 
on the other hand, it would become at a blow equal to the disjunction ' A is 
either B or C,' and would include in itself the case ' If A is B ' with its con- 
verse. In other words, it would become a reciprocal judgment, correlative to a 
definitory affirmation, and as such would admit of conversion or inference by 
denial of the antecedent ; just as if we were to infer from 'A is B ' that ' not- A is 
not-B.' This, as we have seen all through, is the ideal of the judgment ; and 
a hypothetical judgment with negative condition or negative consequent, that 
fulfils this ideal, coincides already with the disjunction. But usage does not 
warrant the ascription to the hypothetical ' If A is not B it is C ' of the meaning 
1 If A is not B-without-C it is C-without-B.' As commonly employed, there- 
fore/it lays down a certain outer limit, but does not exhaust the subdivisions 
within the limit. This is just the point of contrast between the hypothetical 
judgment in its ordinary signification and the complete disjunction. But there 
is a certain tendency on the part of the former to advance towards the latter. 
It is plain that the reasons which induce us to give prominence to the alterna- 
tives mentioned as the only ones to be specially considered may readily 
transform themselves into reasons why only the alternatives mentioned can be 
considered, or, perhaps, can exist. We have such reasons just warranting a 
disjunction in the instance given above (p. 342), where the case formed by the 
combination of the alternatives considered exists, so to speak, in fact but not 
for the law. 

ii. It may be worth while to point out that disjunctions with more than two 
alternatives must be treated, as regards the hypothetical judgments involved, as 
a succession of dichotomies. The hypothetical judgments of each type involved 
in such a disjunction would therefore be equal in number to the disjoined 
members, i. e. each alternative must be made in turn the positive and negative 
condition of an hypothesis, with a compound consequent, the disjunctive*nature 
of which cannot appear in the hypothetical judgment. A is either B, C, D, or 
E. Then we have the negative conditions, ' If A is not B, it is within C D E ; ' 
* If A is not C, it is within B D E ; ' < If A is not D, it is within C B E ; ' If A is 
not E, it is within C B D.' The positive conditions will correspond severally 
to the above negative conditions. 

Here we see a second defect of the hypothetical as compared to the disjunc- 
tive judgment. It can only handle one reciprocal relation at a time, and cannot 
master a whole system of such relations in a single view. In the above analysis 
the hypothetical judgment does not enable me to express more than a single 
contradictory relation, as between a particular A and its not-A. The idea of a 
pervading contradictory relation, characterising any one part as against all the 
others, cannot be expressed in any one hypothetical judgment. By saying 

chap, viii.] Disjunction and Conjunction. 349 

The reference to these two or four hypothetical judgments 
has its value in elucidating the nature of the system which 
a true disjunction embodies. It exhibits in the plainest 
light the indispensable function of negation in articulated 
knowledge, and the positive import with which in virtue of 
that function the negative is invested. We have already 
seen the nature of this import in the analysis of the signifi- 
cant negation, where, however, the positive ground and 
consequence of denial were matters of tacit understanding 
and inference from context. In explicit disjunction, on 
the other hand, we find them after they have been de- 
veloped independently and distinctly in the hypothetical 
judgment, and affirmed as actual attributes within a system 
that is alleged to exist in reality. 

iv. But, it may reasonably be objected, it is not in every When are 
system that the parts are disjunctively related. As a rule wliveiy 
the parts of a system are predicable in conjunction and not related? 
in disjunction. 

Apart from the case of intentional abstraction by which 
any conjunction can be turned into a disjunction for in 
the last resort within every system every part involves the 
whole nature of the system this criticism is just. A human 
body is made up of trunk, limbs, and head ; not of either 
trunk or limbs or head. The government of a civilised 
nation consists of the legislative and the executive power, 
not of the legislative or the executive. A genus, again, 
may be said to be identifiable with all its species, not 
merely with either this or that, though here we are on more 
doubtful ground. Triangles are isosceles, scalene, and 
equilateral. Men are white, black, and yellow. We could 
hardly say however that ' the triangle is isosceles, scalene, 
and equilateral,' or that ' man is white, black, and yellow.' 
The difference between conjunctions of the kind here brought 
forward, and true dis) unctions, is formally speaking a differ- 
ence of the aspect in which a real system is regarded, but 

1 If A is not B, it is either C, D,orF' we should be pressing the hypothetical 
type beyond its powers. 

350 Disjunction and the statement of Chances, [booki. 

materially, therefore, has an intimate dependence on the 
actual nature of the real system in question, which may be 
such as to throw one aspect or another prominently forward. 
Every universal may have its differences conjunctively 
enumerated, whether they are in time or in space, or merely 
distinct in thought. But in so far as the universal itself 
enters as a whole into each difference, which it can do in 
very different degrees, so far each difference, if imposed 
as a condition on the universal, excludes all the other 
differences. A man's having a hand does not interfere with 
his having a foot. But a man's having a feeling in his hand 
does begin to make a claim on the universal, the man him- 
self, which is to a certain limited extent incompatible with 
his having a feeling in his foot or elsewhere. And when we 
come to consider such acute interest or feeling as occasions 
the absorption of the whole mind in the perceiving or suffer- 
ing member, then it is true to say, ' The man perceives or feels 
either with, eye or with ear or hand or foot,' as the case may be. 
So again if we think of a triangle as a mere abstract gener- 
ality that describes a heap of various figures, we may say 
that it includes, or that in a collective judgment its in- 
dividual instances are> this, that, and the other. But if we 
think of it according to its complete conception as an 
individuality that must necessarily take individual shape, 
and if we follow the process by which such shape must be 
determined, then we can only express our insight by the 
use of the disjunctive ' Either or.' 

The conception of the whole as conditioned by one of its 
parts takes the place of that imaginary reference to an 
atomic point of time which has been supposed to be of the 
essence of disjunction. 'A moving object is either here or 
there ' means ' if here, not there ' and ' if not here, then 
there.' It does not mean * Within the indivisible moment 
in which I am judging a moving object can be in one place 
only.' For I cannot judge in an indivisible moment, nor 
can I refer to a present that is an indivisible moment. In 
any extended time a moving object traverses space, and 

chap, viii.] The Ultimate Disjunction. 351 

our ' present ' is always an extended time. And so the 
disjunction if referred to our ' present' time would not be 
true, and the moving object would be, like Sir Boyle Roche's 
bird, ' in two places at once.' 

v. When we have understood the nature of disjunction Is the dis- 
there is not much profit in asking whether the disjunctive reducible 

judgment can be ' reduced ' to two or more hypothetical to Hypo- 
, , 1 1 1 r . theticals? 

judgments. The mere fact that the hypothetical in ques- 
tion 1 are separate judgments, and that the disjunction is 
a single judgment, is enough to show that we have in the 
latter a combination of unity with reciprocal exclusion which 
we have not in the former. I have endeavoured to express 
this unity y representing the disjunction as a combination 
of the generic and the hypothetical judgments. But it 
must be remembered that at best we are dealing with 
grammatical types which are only the symbols of states 
of knowledge ; and it is most probable that any one who is 
able to make the two complementary hypothetical judg- 
ments ' If A is B it is not C ' and ' If A is not B it is C,' 
supplies out of his own mind the systematic relation which 
the two taken together involve, in a judgment equivalent 
to ' A is either B or C 

Not to dwell longer than I can help on formal points,. I 
merely remark in addition to what was said above 2 , that 
in any case these hypothetical themselves presuppose the ^ 

ultimate or formal disjunction, ' A is either B or not-B, 5 by 
their introduction of a negative relation into knowledge ; 
and that further, if we wish to take the two hypotheticals 
above mentioned as implying the two which follow from 
them by denying the consequent, we are once more relying 
on this formal disjunction, which is essentially involved in 
such a transition 3 . The material importance of the whole 
question lies in the process by which the form of disjunc- 
tion, in itself on a level with or consisting in the Law of 

1 See foot-note, p. 348. 2 p. 348. 

8 See the account of Contraposition, above, chap, vii : the process by ' denying 
the consequent ' is essentially the same with this. 

352 Disjunction and the statement of Chances, [book i. 

The state- 
ment of 

of the 
in present 

Excluded Middle, i.e. of contradictory opposition *, acquires 
the material significance of Disjunction between positive 
contraries. I have tried to show above that these two 
elements, the bare rejection and the positive contrary, are 
probably to be regarded as distinguishable from the first, 
but as tending to coalesce, and not as later and earlier 
phases respectively of the same movement. Or if, in 
history, earlier and later, then the later, the abstract formal 
negation or bare rejection, is to the earlier, the actual choice 
between positive alternatives, as a separable outgrowth 
which consciously reunites with it in the region of reflective 
intelligence. No anthropological doctrine can affect 
though it may elucidate the above logical analysis of the 
relation between the negative and its material import as 
made explicit in the judgment. 

i: The statement of chances is a case of the Disjunctive 

i. The title which I place at the head of this section 
indicates the limits of the question which I propose to treat 
in it. The calculus of chances, like all mathematical 
reasoning, has at its root an inference that can be expressed 
in ordinary language. In treating of inference it will be 
incumbent upon us to discuss the differentia which sepa- 
rates calculation from ordinary reasoning ; and we shall 
find the outward and visible sign of this differentia to con- 
sist in the enormous abbreviation of reasoning processes by 
their condensation into the import of recognised symbols. 
It is a further question in virtue of what peculiar nature an 
inferential process can submit to such an abbreviation, and 
also to what extent the abbreviation has the effect of substi- 
tuting something else, e. g. application of a rule-of- thumb 2 , 
for the reasoning process so ' abbreviated.' But the value 

1 It is an nnlucky confusion that the so-called law of Contradiction only 
explains Contrary opposition, and that it is the law of Excluded Middle that 
lays down the principle of Contradictory opposition. See Bk. II. chap. vii. 

2 I have in my mind as an instance the use of tables of logarithms. It does 
not appear formally essential that any one who uses them should understand 
the reason of the rules he applies, i. e. (I presume) the nature of Indices. 

chap, viii.] Concrete and abstract Disjunction. 353 

of any such abbreviation must ultimately rest in a logical 
sense upon the reasoning which it represents, and this 
reasoning must be in its nature explicable in language like 
any other reasoning 1 . Thus in the calculus of probabilities, 
though I am obliged from mathematical incompetence to 
omit much that might be of interest to an expert even 
from a logical point of view, yet the principle of the state- 
ment of chances is not a matter of technical method, but of 
fundamental postulates of knowledge. And also, no doubt, 
it illustrates the necessity by which totalities of a certain 
degree and kind of abstraction become subject to numerical 

ii. The statement of chances rests upon a species of dis- Affiliation 
junctive judgment, but not on what we have spoken of as distinction. 
the true or real disjunction which might also be called, in 
contrast with that which we are about to discuss, the con- 
crete disjunction. The concrete disjunction, in as far as it 
reaches its ideal, embodies differences that are distinct and 
individual modifications of the underlying system, and pro- 
vides in the nature of the common subject a complete 
account of the conditions which determine it to each of 
these differences. In using such a disjunction we know 
precisely how and why the whole or real subject must enter 
into each of the differences which constitute it. And though 
it may be said that we do not or need not know when or 
how far each condition involved is or can be real, yet we 
must know something of the relation of such conditions 
to the reality of the system which they affect (because their 
reality is partly relative to its reality), and at least there is 
no sort of reason for supposing that the reality of these 
known conditions is to be taken as an equal amount in 
the case of all the several alternatives. The variety of the 

1 A practical reservation must here be made in considering the higher 
mathematical processes from this point of view, because they may presuppose 
a number of stages consisting of subordinate processes, and be inexplicable 
apart from these latter. But to explain the whole complication in ordinary 
language might involve a lengthiness that would make it harder to follow such 
an explanation than to master the proper mathematical language. 
VOL. I. A a 

354 Disjunction and the statement of Chances. [Booki. 

world and of all reality throws the whole presumption the 
other way. The idea of equally grounded alternatives is a 
negative idea, and can only exist by a defect of knowledge, 
or by an abstraction from what we know. 

The abstract disjunction, on which alone a statement of 
chances can be based, cannot be a system of alternatives 
whose conditions and relations are thoroughly understood. 
It is rather allied to what was spoken of above as the dis- 
junction of ignorance. The affiliation to the hypothetical 
judgment is indeed the same in all disjunctions that are 
formally perfect, i. e. both exclusive and exhaustive. But 
on its other side the abstract disjunction does not, like the 
concrete, descend from the generic judgment with its pene- 
trating and dominating individuality, but rather from a 
judgment of enumeration such as the collective judgment, 
with' its homogeneous parts which do not occupy individual 
or distinctive relations to the containing identity. It is true 
that to give meaning to any disjunction, or to a statement 
of chances founded upon it, the parts or members of the 
whole must be distinct as well as homogeneous. But the 
distinction is in this case mere distinction, interesting as a 
result, like the differences between the six sides of a die, 
but on the side of its relation to the whole not rooted in 
any known modifications of that whole. In other words, 
the number of parts, or the fact that each is one among so 
many, is the primary fact, and their 7ialure is secondary. 
We may illustrate this by contrasting an example of a con- 
crete with one of an abstract disjunction. ' The constitu- 
tion of a modern nation,' it may be said, ' is necessarily 
either democratic or plutocratic.' Here the fact that the 
species assigned are two in number is of no importance. 
No one would think of trying to infer anything from it as 
to how many nations were likely to be democratic and how 
many to be plutocratic. The whole weight of the judg- 
ment rests upon the component elements implied in 
' modern nation,' and upon the development of those 
elements which the judgment indicates to be necessary. 

Chap, vin.] Equal grounds of Affirmation. 355 

But if we take such a judgment as 'A die must turn up 
one of its six sides ' we here regard the individuality of the 
several sides as indifferent with respect to the probability 
of their recurrence, though not with respect to its results. 
The important matter is the number of the alternatives. 
For either we are unable to estimate the operative causes 
which determine one alternative rather than another, or we 
wilfully abstract our attention from them for the sake of 
falling back on a more general process of estimation. We 
are to suppose then that as the basis of our statement of 
chances, we have before us such a formal disjunction as the 
above, closely akin to the judgments which arise in the 
process of enumeration, but w r ith the addition of those 
known relations between the enumerated parts which are 
embodied in the hypothetical judgments with negative 
antecedent and consequent respectively. 

iii. We are then in a position to enter upon a process which Essence of 
I can only describe as taking stock of our knowledge by ment f 
arithmetical methods. We know that the die has six sides chances, 
and no more, and that as the result of a single throw it 
must turn up one of them. We know that we do not know 
of any cause operative in the nature of the die or in the 
conditions of the throw that should favour any particular 
side, nor of any grounded presumption whatever in favour 
of any one side in particular. In the case of the die, which 
herein differs from many cases of the statement of chances, 
we may say that we know that there is not any permanent 
operative cause either in or outside the die that can favour 
one event in particular. Therefore and here is the all- 
important step which really constitutes the statement of 
chances we go from ' no known inequality of the grounds 
for affirmation 1 ' to ' equality, so far as follows from this 
knowledge, of the grounds for affirmation ' of the several 

1 Judgment about the future, if we judge, is of course affirmation as much 
as judgment about the past. But it is not essential to the statement of chances 
to refer to the future. They can be stated on given premises about any event, 
although its real issue be known. 

A a 2 

356 Disjunction and the statement of Chances, [booki. 

alternatives. Having made this step, i.e. having placed 
the grounds for each alternative on a level as equal, we are 
of course free to treat them as units, and a ratio expressing 
the relation of each to all follows as a matter of course. 
Each alternative counts for one, and none for more than 
one. In other words, the ground for the affirmation of 
each, assuming the reality of the common subject, is repre- 
sented by a fraction of which i is the numerator and the 
total number of alternatives the denominator. We do not 
attempt to say what the ground is, but we say that, by the 
terms of the disjunction, it is one out of so many equal and 
reciprocally exclusive grounds. This transition from in- 
difference of formulated knowledge to equality of grounded 
affirmation, and so to the relation of units within a sum 
total or fractional parts within unity, is the logical foundation 
on which the statement of chances rests. 
Applica- iv. All its developments are applications of this prin- 
statement 6 ciple. a. For instance, it may happen that alternatives 
as calculus, which are separate units in respect of the ground for 
Altema- a fft rm { n cr their reality are identical in respect of that result 

tives and & J r 

Results. of which the chances are being stated. It follows that the 
chances of this result are represented by as many units 
out of the sum total as there are equal alternatives which 
produce it. In other words, the chances of the common 
consequence of a number of alternatives whose chances are 
known is the sum of the chances of those alternatives. If 
you bet with me that you will throw a six first throw 
with a single die, then all five alternatives from one to 
five inclusive have annexed to them the consequence that 
I win the bet. The total number of alternatives being 
six, I have thus J- of the chances in my favour, or the 
chances against you are 5 to i. 

The further processes of the calculus must always reduce 
themselves to obtaining a correct enumeration of the equal 
alternatives, and a correct estimate of the number of those 
equal alternatives which have annexed to them the result 
whose chances are to be stated. 

chap. viii..] Physical Alternatives, 357 

j3. The combined chances of independent events illus- Physical 



trate both these principles very simply. 

To find the physically different throws that are possible 
with two dice, we must take into account which is which of 
the two dice. It is obviously possible in a single throw for 
any side of the one die to concur with any particular side of 
the other die, i. e. writing down the six sides of the one die 
as headings, you will have to write down all six sides of the 
other as possible cases under each of these headings. This 
relation is of course expressed numerically by multiplying 
the whole number of sides of one die by the whole number 
of those of the other: 6x6 = 36. This gives the correct 
enumeration of the alternatives that are physically possible, 
the chance of each in case of a single throw being ^\. 
Generalising this process, we may say that in two or more 
independent sets of alternatives the chance of the concur- 
rence of two or more particular events, as many as there 
are sets concerned, is determined by the product of the 
numbers of alternatives forming each separate set multi- 
plied together. That is to say, the chance of any par- 
ticular concurrence of events, consisting of one out of each 
independent set, is 1 divided by the product in question. 

y. But to return to the example of the two dice, it interesting 
may be that the 36 possible concurrences would not all results - 
count as different, because e. g. the throw 2 with the 
die a and 1 with the die b may be treated as the same 
with the throw 1 with a and 2 with b. Therefore the 
results which are the alternatives according to this mode 
of counting have not all of them the same chances in their 
favour, i. e. do not severally contain the same number of 
physically distinct alternatives. Each of the six throws 
1 and 1, 2 and 2 &c. up to double sixes inclusive corre- 
sponds to one physical alternative only out of the possible 
36, and therefore has only the chance represented by ^V 
On the other hand, each of the fifteen ' throws ' 1 and 2, 
1 and 3 to 1 and 6 inclusive, 2 and 3, 2 and 4 &c. to 5 and 6 
inclusive, is a lesult annexed to two physical alternatives 

358 Disjtcnction and the statement of Chances, [booki. 

(1 and 2 or 2 and i,&c), and therefore counts as two equal 
cases or units, and has a chance represented by the sum of 
the chances of these equal cases, viz. by i\. instead of ^V 
These 15 ' throws ' then, answering to two actual alternatives 
apiece, exhaust the 30 real cases that remain after deduct- 
ing the six doublets, and the whole 36 alternatives are thus 
accounted for. Or again, if we take into account merely 
the number of points thrown at each throw, without regard 
to their distribution between the two dice, we get six com- 
binations of throws that will give seven points, five for eight 
points and six points respectively, and so on to one com- 
bination for two points and twelve points respectively. The 
chances of throwing 7 are therefore 6 e, and of throwing the 
other numbers ^V> *V an< ^ so on down to V respectively. 
What does v. Logicians are not agreed as to the proper description 
st f a ^ ment of that which is expressed by the ratio that embodies a 
represent? statement of chances. Their disagreement arises more 
from the subtlety of the distinctions involved, which makes 
description difficult, than from a substantial difference of 
opinion as to the relation between reality and the cognitive 
act in question. It is not unnatural, for example, to say 
that the ratio expresses our subjective expectation. But 
this is an obvious slip, because the whole process of the 
statement is undertaken in order to correct and control 
our subjective expectation, and is futile unless it does so. 
The complete counterpart of this idea would consist in 
maintaining that the ratio expressed an actual behaviour 
on the part of real things. I do not know that this sug- 
gestion has ever been made in this extreme form. Som( 
thing of the same kind however is commonly believed wil 
respect to the realisation of chances in a series, which 
shall speak of directly. 

The ratio of chance seems really to express the amoui 
of ground, which is afforded by the knowledge for -mutated in 
the disjunctive basis of the calculation, for affirming the 
reality of the result whose chances are in question, on the 
assumption that the general case, which forms the subject, 

chap. viii. j True problematic Judgment. 359 

is realised. Instead of amount of ground ' it would be more 
usual to say ' degree of probability.' And by avoiding the 
expression probability we do not really escape the tautology 
which it would introduce. For the idea of a measurable 
amount of logical ground, like the idea of a measurable 
degree of probability, is only intelligible with reference to 
the statement of chances. 

1 Expectation ' sounds more like a term which might 
elucidate the definition, and if we say that the statement of 
chances represents the expectation which is justified by the 
premise, we might not be far wrong. But I do not feel 
sure that anything can be meant by a degree of expecta- 
tion except the mood, whatever that may be, which is 
founded upon a statement of chances. So that the chance 
would not come from measuring the expectation, but the 
expectation from measuring the chance. Even if we identify 
expectation with judgment a proceeding which is more 
than doubtful we cannot say that the chances necessarily 
represent the degree of certainty with which we judge in a 
statement of chances ; because the statement, giving due 
numerical weight to every equally-grounded alternative, 
asserts in the proper ratio the reality of all the alternatives, 
and is in this aspect a judgment with its conditions made 
fully explicit, and therefore necessary or apodeictic. Net 
that a statement of chances is usually or ever true in fact ; 
but this divergence from fact, or abstract character, affects 
the categorical aspect of the whole disjunctive basis of the 
statement, the truth of which basis is in no way affirmed 
or impeached by the ratio of chance founded upon it. The 
chance that one side of a 6-sided die will turn up is \ ; but 
this says nothing about the certainty that there is a 6-sided 
die. Paradoxically enough, the statement of chances seems 
to measure, if anything, the degree of certainty of a pro- 
blematic judgment made without knowledge of or in ab- 
straction from the statement, as to the probability of a 
single alternative out of a number without reference to the 
remaining alternatives. Not that a statement of chances 

360 Disjunction and the statement of Chances, [book i. 

can govern the meaning of a judgment made in ignorance 
of it, and it is indeed hard to see any meaning in degree of 
certainty apart from measurement by the enumeration 
which gives a ratio. But on the other hand, the moment 
we have the ratio, we have with it the whole consequence 
of the assumed reality, and the judgment which asserts the 
ratio is mere arithmetical necessity, the nature of the 
assumed reality being given. The judgment that ' the odds 
against any one side of a (6-sided) die turning up at one 
throw are 5 to 1 ' has not a probability as 5 to 1, but on 
the premises is necessary. But it determines what I ought 
to mean, when I say, in ignorance of or not considering the 
calculation, ' it is unlikely that a six will turn up the first 
throw.' If I reflect and say, ' It is unlikely (with an un- 
likelihood of 5 to 1 ) that etc.,' then my judgment has ceased 
to be problematic, and has become necessary, i. e. the con- 
ditions of its probability are analysed and made explicit. 
Thus probability as a character of judgment disappears 
when measured. 

The ratio of chance then expresses the amount of ground 
for affirming, that follows from the knowledge formulated as 
the disjunctive basis of the reckoning. We may possess 
knowledge that does not conform to the conditions of the 
statement of chances, or at least that is not relevant to the 
special disjunction which we are able to employ. Such 
knowledge may cause us to distrust the reckoning slightly 
or wholly as it affects some particular case. I may think 
for instance that the calculated risk of being run down by a 
cab in the streets of London does not apply to one man 
who is in the prime of life and habitually alert, or to 
another who is bedridden and never goes into the streets 
at all. But none the less the probability of cab accidents 
for each individual of the population on the data that are 
taken is a mere question of calculation and can only have 
one correct answer. My private notion that I have supple- 
mentary data which ought to be considered, or that a more 
careful distinction should be made between classes of per- 

chap, viil] Actual Series. 361 

sons in the data, does not in the least affect the probability 
which flows from the premises in any particular calculation. 

The calculus of chances, in short, bears the character of 
the judgments from which it is derived. Like the pure 
hypothetical judgment, and the greater part of the abstract 
judgments derived from the judgment of enumeration, it 
affirms of Reality indirectly and conditionally. Its truth 
is a truth of necessity, a consequence that follows from a 
selected or fancied character when taken as real. Such a 
consequence is not subjective or arbitrary. Given the 
premises, it can only be drawn in one way, and every other 
result from those premises is wrong. But yet it does not 
express actual concrete fact. It expresses a truth necessi- 
tated by the nature of Reality, but not as it stands em- 
bodying a fact of Reality. It is simply an arithmetical 
consequence of a highly abstract disjunctive enumeration. 

vi. In every statement of chances we admit our partial Chance 
ignorance. If this were not so, the statement would in- s" r i e g Ctua 
volve a flat contradiction. For our grounds for affirming 
reality are equal in the case of all the alternatives, and yet 
our statement of chances is based on the assumption that 
only one of them can be realised. 

a. But if we do not bear in mind the proportion of ignor- Fallacies 
ance which enters into our data, we are tempted into two series" 2 10 
fallacious attitudes. 

In the first place, we consider ourselves justified in being 
astonished at the realisation of the alternative which has 
very few chances in its favour. 

And in the second place, we palliate the apparent con- 
tradiction between equal grounds for reality and unequal 
realisation by affirming that the statement of chances has 
genuine truth only in an actual series which realises all the 
equal alternatives equally. To realise all the equal alterna- 
tives equally is of course the same thing as to realise all 
the interesting results 1 in the ratio prescribed by the state- 
ment of chances. 

1 See above, p. 357. 

362 Disjunction and the statement of Chances, [book i. 

First, then, we have very small ground for being sur- 
prised at the actual occurrence of that alternative which 
had fewest chances in its favour ; and absolutely none for 
being surprised at the occurrence of a marked or interest- 
ing alternative which has against it enormous odds, but 
only the same as against every alternative which can pos- 
sibly occur. In the former case we are cherishing a private 
presumption that the knowledge embodied in our premises 
represented the actual operative causes which determined 
the realisation of one or another alternative, and this is ex 
hypothesi not the fact. In the latter case we are misled by 
a special interest into comparing, as if they were cases of 
which the chances should be equal, cases which are not 
' equal alternatives,' but ' interesting results ' comprising 
unequal numbers of equal alternatives, viz. on the one side 
a single case which is in some way remarkable, e.g. a hand 
at whist consisting solely of trumps, and on the other side 
all other possible hands whatever, which we implicitly con- 
trast, as a single case, with the opposite ' interesting result.' 
We are therefore surprised at the immense adverse odds 
in spite of which this result has been realised, not re- 
flecting that there are precisely the same adverse odds 
against any one of the alternatives which occur in every- 
day experience, though not, of course, against all of them 

And secondly, the realisation of the ideal alternatives in 
a series of real cases is confessedly a fiction unless we stop 
the series at an arbitrary limit say, for instance, the 
actual limit of individual objects or events in question in 
space or time and even within this limit the series is not 
what we want. 

There are under this head of an actual series two possi- 
bilities which prima facie at least must be distinguished. 
We may have to deal with a natural or deductive cycle 
of alternatives, or with an arbitrary or inductive cycle. 

In what may be called a natural cycle the alternatives 
are ideal cases that follow obviously from the nature of the 

chap, viii.] Verification by Experience. 363 

general subject ; and are distinct from the real cases, the 
actual instances or events, which may or may not con- 
tinue to present themselves beyond the one real case which 
is postulated in the statement of chances. The sides of a 
die or of a coin furnish ideal cases ; the throws of a die or 
tosses of a coin are real cases. The natural cycle is the 
lowest number of actual events in which the ideal alterna- 
tives could be all realised equally ; i. e. six throws in the 
case of the die, two tosses in the case of the coin. Beyond 
this natural cycle there is nothing to suggest a limit to the 
series of real cases. We have therefore to ask, in consider- 
ing the verification of natural cycles by experience, whether 
the real cases correspond to ideal cases (i) within every 
natural cycle that is observed ; and (ii) in the series as a 
whole continued without limit. 

In what, on the other hand, may be called an arbitrary 
cycle the ' ideal alternatives ' are derived from the enumera- 
tion of real cases. The population of Great Britain at a 
given date would be such a collection of real cases, and 
that these real cases are identical with the equal ideal 
alternatives is shown by the fact that their number forms 
the denominator in the fraction that states the chances. 
If e. g. the population were 30,000,000, and 600,000 
people died in the year, the chance, assuming constancy of 
the average \ that any one individual taken at random 
would die within the following year would be -3^0-77^0-0' vlz - 
-sV The analysis of such a statement of chances appears 
to me not quite simple, and I doubt whether Mr. Venn, in 
maintaining that chance essentially refers to series, has 
identified its elements rightly. The individual human 
beings composing the population in question, in whatever 
order we choose to take them (say, in the accidental order 
of our enumeration), must correspond, I think, both to the 

1 Or following what was said above of the independence of calculation and 
real event, we may neglect the constancy of averages, and say, referring to the 
same year for which the enumeration is taken, ' the chance that any particular 
individual will have died in that year.' On the same premises, the chance is 
the same after the event as before it. 

364 Disjunction and the statement of Chances, [book i. 

real case 1 the throw of a die or toss of a coin and also to 
the ideal cases to the sides 2 of the die or of the coin 
considered as possible alternatives. And the two general 
cases of dying or not dying within the year cannot I think 
correspond to the equal ideal cases or possible alternatives, 
but must be treated as those combinations of alternatives 
which arise when several possible ' ways in which the event 
may happen ' have an identical consequence in which we 
are interested. Or, in short, we might put it thus, follow- 
ing in part Mr. Venn's interesting discussion : English 
humanity is the ' event ' ; each individual is ' a way in 
which the event may happen 3 ; ' dying and not-dying or 
male and female 4 are general consequences or results each 
of which emerges from a large number of 'ways in which 
the event may happen.' Thus, as is right in theory, the 
ratio of chances is determined by the number of ways 
in which the event may happen, which in these arbi- 
trary cycles = the number of cases in which the event 
does happen. It is a consequence of the inductive 
character of the cycle that this number of ways has 
no obvious and necessary meaning, but is a mere in- 
ference from the number of times that the event does 
happen. It is as if there was a die of unknown structure 
thrown 30,000,000 times, and exhibiting a white side 
29,400,000 times and a black side 600,000 times. If then 
we chose to assume that we had before us a die with 600,000 
black sides and 29.400,000 white sides, and to estimate all 
further chances on that basis, we should be in an analogous 
position to that which we adopt when we calculate chance 

1 This is what Mr. Venn describes (Logic of Chance, chap. i. sect. 6 ; chap, 
iii. sect. 33), in the ordinary language of the theory, as the ' event,' and in his 
own language as the collection of attributes. 

2 This is what Mr. Venn describes either as ' a way in which the event may 
happen,' or as the ' occasional attribute.' 

3 Or a particular modification of the collection of attributes by occasional 

* Mr. Venn, Logic of Chance, chap. i. sect. 6. Male and female are not the 
' ways in which the event may happen.' This would give the chance of each 

chap, viii.] Adherence to a Ratio. 365 

on the basis of a ratio observed de facto in a cycle of 
cases. The chances of white and black respectively are 
then %% and T V on the basis of this real but arbitrary 
cycle, regarded as the foundation of an ideal cycle of 
alternatives identical in content with itself. 

Now the arbitrary cycle itself, the 30,000,000 individuals 
and 6co,ooo deaths, being given as real, there is no question 
of its correspondence with a pre-established ratio. If we 
ask whether the ratio of T V which it prescribes is realised 
in experience, we can only mean to enquire whether the 
distribution of the deaths is regular within the observed 
cycle, or whether the same ratio prevails outside this real 
cycle, which latter question may be followed up if we 
please by the same question as before about the regularity 
of occurrence. I am not quite sure that in speaking of the 
uniformity which attends large numbers of instances our 
writers always remember that such uniformity demands 
the comparison of two or more cycles. The ratio of 
results within a single group, even if embracing all hitherto 
observed instances, is in the absence of an antecedent rule 
a mere fact and not a realisation of anything. Every 
ratio is definite, and any two numbers have a ratio, so that it 
is a truism to speak of a definite ratio as prevailing between 
classes of cases in a single group \ Within a single large 
group if we speak of adherence to a ratio, we can only 
mean regularity of occurrence. And in the case of indi- 
viduals that are not events in time the significance of such 
regularity and its existence must depend simply and solely 
on the order in which we consider and enumerate them. 

Thus the two kinds of cycles or groups of instances seem 
to be quite differently situated with respect to empirical 
verification, i. A natural cycle from the first corresponds 

1 Logic of Chance, i. 6. The distinctive characteristic of probability is that 
occasional attributes as distinguished from permanent ones are found on ex- 
tended examination to exist in a certain definite proportion of the whole number 
of cases. The italics are Mr. Venn's. How could they exist in anything but 
a definite proportion ? 

366 Disjunction and the statement of Chances. [Book i. 

or does not correspond to its antecedent law, within the 
limits which that law spontaneously prescribes. If we 
throw all six sides of a die in every six throws there can be 
no doubt that up to the point when we break off the series 
is an empirical verification of the chances as we stated them. 
It shows that the unknown causes operate equally, and thus 
produce the result, which we anticipated by neglecting 
them. But in treating of actual experience we may prac- 
tically disregard this kind of correspondence, which is not 
common in fact and at all events could hardly repeat itself 
through an extended number of observations. 

ii. We are thus referred to the second question which we 
mentioned as capable of being proposed respecting a natural 
cycle, viz. whether the law which it presupposes (e. g. every 
side to turn up once in six throws of a die) is realised in the 
long run. It must be observed that to speak of realisation 
in the whole set of actual cases, whatever their number may 
be, cannot furnish a standard in this question, because this 
number is constantly varying and is very different in 
different subject-matters. There is nothing between reali- 
sation in every natural cycle and realisation in an infinite 
series if we keep clear of causal presumptions which do not 
belong to the reckoning of chances pure and simple. There 
is no doubt that the law presupposed by a natural cycle 
may be realised in a great and increasing number of obser- 
vations, and that inferences may with the aid of causal 
presumptions be drawn from this realisation. But for all 
that, it is simply nonsense to speak as if the true and 
only true realisation of a ratio of chance was in the series 
of real instances continued ad infinitum. Mr. Venn, who is 
consistent in regarding this as the solution of the antithesis 
between equality of ground and inequality of reality, denies, 
as I understand him, that the formula \^ has any meaning 

1 Mr. Venn seems to have been influenced by considerations such as those of 
p. 360 above. It is true, as there shown, that the judgment which measures 
probability loses ipso facto that isolated reference to a particular alternative 
which marks the genuine, or at least the natural problematic judgment. In 

chap, vin.] The arbitrary Cycle, 367 

as applied to a single real throw of a die, except by associa- 
tion with the idea of a series in which all sides should 
equally be exhibited. Here we come into the province of 
fiction. There is no reason, in the cases before us, that such 
a series should be a fact at all. And in these and in all 
other cases alike it is impossible that the infinite series could 
be a fact. And yet, if not a fact, it fails to solve the anti- 
thesis as a solution of which it is propounded. It is not in 
fact possible to go on trying for ever, and it is not in theory 
true that supposing we did go on trying for ever (abstracting 
from the contradiction involved) every alternative must be 
realised according to the ratio. The ratio may be justly 
erected according to our grounds of knowledge, even if 
some of the alternatives are absolutely impossible and 
therefore could never occur although, per impossibile, the 
series of trials should be prolonged to infinity. 

In the case of the arbitrary cycle the answer to the ques- 
tion is still less favourable. The primary interest of the 
arbitrary cycle is just in that statement of chances affecting 
individual real cases which is suggested not to be the true 
meaning of the ratio. There is in this case no antecedent 
law between which and the real cycle a correspondence 
could be observed. The real cycle itself is and prescribes 
the law. And although cycles of real events that fall out- 
side it, or minor cycles within it, can be tested and compared 
with it in respect of the ratios they display as we compare 
the ratios of deaths to population in successive years yet 
it is not easy to say on what ground the first cycle that we 
happen to observe should furnish a rule to which subse- 
quent cycles are expected to conform. The whole group of 

every statement of chance we have an apodeictic judgment involving the entire 
content of a disjunction in the bearings of its members upon one another (as 
condition and consequent). So far Mr. Venn and I are together. The question 
therefore reduces itself to that of the purport with which the reference to the 
remaining alternatives is charged, whether it depends on the idea of a completed 
series, or can be explained by the (assumed) equal claim which each alternative 
makes on reality in virtue of the (assumed) equality of their grounds. The 
latter view seems to me to be demanded by the nature of the abstraction on 

I which the whole idea of stating chances depends. 

368 Disjunction and the statement of Chances, [booki. 

observed events or individuals is a comprehensive fact, within 
which the ratio of the ways in which they happen or of 
their classes is also simply a fact. Any comparison which 
we may make of the ratio exhibited in minor cycles within 
this entire group has only the interest of the comparison 
between different groups of actual occurrences or indi- 
viduals 1 . On the assumption that the operative but un- 
known causes are not changing progressively, or that we 
can allow for their progressive change, we may no doubt 
expect to find that a ratio which we elicited from case i to 
iooo will hold good for cases iooi to 2000. But if what we 
want is merely the serial form, we have it already in cases 
1 to 1000 ; while if what we want is the multiplication of 
observations, why should the 2000 cases a wholly arbitrary 
number be especially satisfying ? The fact is, that when 
we have the serial form given to begin with, as in these 
arbitrary cycles, or groups of instances limited only by our 
ceasing to enumerate them, we see that it omits just that 
peculiar transition which is the essence of the statement of 
chance. It only presents us with this transition in so far 
as, surrendering its serial form, it becomes the basis of a 
fractional expression which summarises our knowledge, 
drawn from the series, with reference to some instance or 
instances whether within or external to itself. This criticism 
applies to the serial form as such. The equal realisation of 
alternatives considered as equal (i. e. apart from regularity 
and irregularity, which are equality and inequality as judged 
by minor cycles) destroys the peculiar relation of equal 
knowledge to unequal fact, which is the ground of chance. 

On the infinite series, or approximation in the long run, 
I can say no more than I have said above, and others have 
said before me. The thing is simply a fiction, and the 

1 Mr. Venn, Logic of Chance, ii. 8, seems thoroughly to accept this result, and 
to conceive that all probability, even in what I have called natural cycles (in 
his phrase ' a priorV probability), is at bottom this and no more. I cannot but 
think that if probability in a specific case means anything, it must, even though 
dependent on an arbitrary cycle, be stated as above in the form of a natural 

chap, viil] Interpretation of Series. 369 

reference of the realisation of a ratio to it proves, if any- 
thing, that it is ultimately necessary to admit that chance 
is independent of a real series. 

/3. The true bearing of a series on the verification or Causal 
corroboration of a ratio expressing probability must consist f^m^ 06 
in its relation to the causal presumptions which dominate Series - 
our judgments about reality. All judgments that deal with 
fact assume, though they may not explicitly assert, causa- 
tion. Statements of chance do not proceed by following 
causation into its ramifications ; we should thus have concrete 
knowledge and not equality of alternatives. But when the 
results of experience coincide with the predictions of the 
calculus, this suggests to us not that we knew the right 
causes or any causes at all, but that the actual causes at 
work have a character compatible with the results which we 
obtained through the indifference of ignorance. If, on the 
other hand, the results of experience deviate widely, so far 
as experience goes, from the ratio suggested by the calculus, 
then though this deviation can never amount to aflat contra- 
diction, yet it suggests an arrangement of causes incom- 
patible with the results which were generated by the 
indifference of ignorance. If we cast six twenty times 
running with the same die, we have no right to say that 
this theoretically speaking contradicts the ratio of chance 
(unless we take as a standard, which no one would ever do, 
the natural cycle of six throws), for in 120 throws the balance 
might be restored. In other words, no sequence is im- 
possible in such a case, nor is one more improbable than 
another, but of course any one sequence is immensely im- 
probable beforehand as against the whole remaining mass 
of possible sequences. And in any marked or so to speak 
identifiable sequence this improbability strikes us as though 
it had occurred in face of some enormous probability in 
favour of some one other sequence, all the less identifiable 
sequences counting as if one in number, though n 1 in 
probability. This is a partial account of our surprise ; but 
as has been well explained by Sigwart, there is in it the 

VOL. I. B b 

37 Disjunction and the statement of Chances, [booki. 

further element that whereas the twenty consecutive sixes 
are on the assumptions from which we started but one 
among an enormous number of equal possibilities, they 
happen to be of such a nature that on another assumption, 
incompatible with those, they would follow with absolute 
or all but absolute certainty. We know that if the die is 
cogged it will always turn up the same side, or to speak 
generally, if there is present an operative cause which 
necessarily produces one alternative, that alternative will 
always be produced. This suggests the comparison between 
one ratio, that with which we started, which gives a very 
minute probability for the result found in practice ; and 
another ratio, formed on a different assumption, which gives 
the observed result with something like certainty. Nothing 
binds us absolutely to either, but it is plain that so far as 
experience has gone the probability is with the latter in the 
proportion in which it gives the result observed with greater 
probability than does the former. It must be carefully 
remembered that here, as all through this discussion, we are 
dealing with hypothetical judgments only. The probability 
I speak of is only on the data taken into account. If I am 
playing with a most respectable friend who says he has got 
the die from a good shop, I may prefer to believe in the 
reality of a peculiar case rather than in a fraud. 
Observed y. I do not see that it is inevitable, as has been maintained, 
an ?f a i" that an observed series must deviate from the calculated 
Series may ratio, as it passes through fragments of a fresh cycle. Of 
comci e. course ft s coincidence with the ratio will not be demonstrable 
while any cases are wanting to finish the cycle ; but if we 
shrink from saying that the observed numbers can coincide 
with the calculated numbers in a half cycle or less, we must 
not, I think, say that they deviate, unless coincidence at the 
next natural cycle is already impossible. Five complete 
cycles of sides and three different sides in thirty-three throws 
of a die surely form a case which should be distinguished 
from the same five cycles of sides plus three repetitions of 
the same side. 

chap. viii.] Chances of Truth a priori, 371 

d. In speaking of the truth of chances based on statistical The series 
averages, we may illustrate what has been said by the f " a ^ y e 
different positions of an insurance office and an individual purposes. 
customer of the office. To the individual whose expecta- 
tion of life is in question the chance of life gives but little 
information, at all events so long as it is large. Whether 
he gains or loses by insuring his life is for him practically 
a mere uncertainty. He knows what it is reasonable to 
expect on the general data of reasoning, but he has no sort 
of ground for being surprised if it does not happen. For the 
office, on the other hand, so long as the averages are con- 
stant, the fate of individuals is wholly indifferent except in 
so far as they are more lightly or more heavily insured. If 
the office could be sure that in each class of customers 
(ranking them by the amount of their insurances) the 
average of deaths would be maintained at the same figure, 
it would make no sort of difference to it who in particular 
died. Thus it is true that in a real cycle the ratio of 
chance may in a certain sense become a fact. What is not 
true is that in becoming a fact it remains a chance 1 , and 
that if it fails to be realised in the short run it must be 
realised in the long run. 

vii. Before passing to the subject of modality I will Probability 

mention an interesting point in the theory of chance, which ^int in the 

is cognate to the above discussions on Privation, Affirma- absence of 


tion, and Exclusion 2 . What statement of chances expresses 
the attitude which we ought to adopt towards an affirma- 
tion in the absence of all knowledge ? The accepted 
answer appears to be i, * for if we make it less than this 
we incline to believe it rather false than true,' or putting 
I suppose the same ground into mathematical language, 
' If we grant that the probability may have any value 
between o and 1, and that every separate value is equally 

1 Cp. Adam Smith's attack on lotteries. You may see, he said, how much 
the chances are against you, by the fact that if you take all the tickets you are 
sure to lose. 

2 Chap. vii. supra. See Jevons' Principles of Science, p. 212. 

372 Disjunction and the statement of Chances, [booki. 

likely, then n and i n are equally likely, and the average 
is always .' I am not prepared to deny this conclusion, 
which of course follows from its data, but I think that it 
may be instructive to discuss these data, which appear to 
me somewhat superficial. It appears that the symbol % 
has also been proposed, on the ground that ' the a priori 
[formal ?] probability derived from absolute ignorance has 
no effect upon the force of a subsequently admitted [real ?] 
probability 1 .' 

It cannot but strike the looker-on that these two sug- 
gested values and \ seem to correspond with the 
conceptions of non-impossibility and of real possibility 
respectively, and that to take probability as having the 
value \ in the absence of all knowledge is analogous 
to conjuring a positive favourable presumption out of an 
absence of counter-presumptions. The question is, accord- 
ing to the analysis of chance which has been stated above, 
whether the two alternatives f true ' and ' false ' are sole and 
equal alternatives. Interpreting absence of knowledge as 
Jevons interprets it, to include entire ignorance of the 
meaning of an enunciation, I do not see that they are sole 
alternatives. { If I ask the reader to assign the odds that 
a Platythliptic coefficient is positive, he would hardly see 
his way to doing so unless he regards them as equal 2 .' 
But to a reader who does not know what the words mean 
and this I suppose is what Jevons intended there is no 
judgment conveyed. The alternative ( unmeaning' must 
then be allowed for in addition to ' true ' and ' false.' This, 
it may be said, makes nonsense of the problem. The un- 
meaning is not a judgment, and the problem is only about 
judgments. Granted ; but then I must not include the 
very large division of the unmeaning in the statement of 
chance without recognising it as a separate alternative. 
And if I am to exclude it altogether I must either be given 
a sentence which I am able to recognise as a judgment, or 
the problem must refer to any judgment as such without 

1 Bishop Terrot, quoted in Jevons, 1. c. a Jevons, 1. c. 

chap.viii.j Effect of Ignorance on Judgment. 373 

considering whether I know beforehand what it is. The 
latter case is not that in question, and could be treated 
perhaps better through statistics of error in the sciences, 
than by deduction from the alternatives ' true ' and ' false.' 
It includes in the reckoning all judgments known to be 
true, whereas the present problem says nothing of these, 
but only of judgments on which being presented to me 
I am unable to return a verdict based upon positive 

The real question then is this. Given a judgment which 
I can understand, but which I have no positive ground 
either to affirm or deny, what are the chances in favour of 
its truth and falsehood respectively? The conditions of 
this problem cannot of course be actually realised, because 
to understand the meaning of a judgment theoretically 
involves some consciousness of pros and con's. Yet there 
are in the world so many almost arbitrary judgments, that 
the question has some importance. Truth and falsehood 
are in this case, the case of intelligible judgments, sole 
alternatives, but I cannot think that they are, under the 
supposed conditions, equal alternatives. I cannot think, 
that is, that every separate value of probability between o 
and 1 is equally likely. For the judgment being a form or 
indeed the form of knowledge, the hypothesis of ignorance, 
in this case ' absolute ignorance,' on which the statement of 
chances is erected, has a peculiar relation to the content of 
such a statement when that content is the judgment. If 
we knew there was a certain motion below a certain limit 
of velocity, but had no further clue to the velocity of the 
motion, it might be true I suppose that every degree of 
velocity below that limit was equally probable. But if we 
know that there is a judgment made, or proposed to be 
made, and have no clue to any degree of positive probability 
in its favour, then for us the zero of probability is the fact, 
and if we were to make the judgment in question it would 
in our mouth be false even if in reality true. Thus, on the 
basis of my individual knowledge, such a judgment quajudg- 

374 Disjunction and the statement of Chances. [Booki. 

ment is by the hypothesis prima facie false. But my know- 
ledge is not all reality, and therefore I dare not say that 
falsity holds the field as an absolute certainty. The possi- 
bility however drawn from the mere difference between my 
knowledge and all reality, is an unmotived possibility; for 
there is at least no antecedent likelihood that my know- 
ledge is always wrong. And I am not entitled to raise 
this unmotived possibility into an alternative having equal 
grounds with the prima facie falsity which follows from 
the hypothesis. 

I am not prepared to suggest any way of representing 
these chances in numbers. Without equally grounded 
alternatives we cannot state chances, and I do not see where 
in this case these are to come from. If one read ' doctrines' 
for judgments, so as to restrict the question to matters of 
some depth and importance, one might obtain interesting 
enumerations out of the history of science bearing on such 
relations as those of false anticipations compared with true 
discoveries. But it would all amount to very little. I only 
desired to point out that the suggested symbols % and \ 
seemed to lie in the track of the fallacy discussed above 1 . 
To say that objecting to a judgment we do not know to be 
true is as unreasonable as accepting a judgment we do not 
know to be true and to say that truth and falsehood have 
a chance of \ each is to say this appears to me to be a 
sophism in the vein of Sir Anthony Absolute 2 . If you 
have no reason for accepting a judgment, you must decline 
to accept it. If you only decline provisionally, and say 
that in future, or to the knowledge of wiser minds, the 
judgment in question may perhaps be proved true, then 

1 See chap. vii. p. 333. 

2 ' Absolute. " Sure, Sir, this is not very reasonable, to summon my affection 
for a lady I know nothing of." 

' Sir Anth. " I am sure, Sir, 'tis more unreasonable in you to object to a lady 
you know nothing of." ' 

Sir Anthony wishes to represent the chances of attachment and non-attachment 
to any unknown lady as each, or even as more than -J in favour of attach- 
ment. This is really not a bad parallel to the view criticised in the text. 

chap, viii.] Symbols for Doubt and Denial. 375 

you unquestionably are cherishing some distinct though 
general presumption in favour of the judgment, and it 
is not one of those whose chances ' in the absence of 
knowledge' we are discussing. We do not treat really 
arbitrary suggestions with so much respect. It seems to 
me monstrous to say that half the equal grounds are for 
truth and half for falsehood when the fact is that you have 
no ground to think the thing true, and require none to 
think it false. 

This brings me to one further distinction. The reader 
ought to reply, ' You do need a positive ground of denial 
in order to deny, and in stating the chances as % you are 
denying, which ex hypothesi you have no right to do.' But 
I suppose that by the symbol % we do not so much deny 
the judgment as refuse to state the chances. It is only the 
logical interpretation of this refusal that brings something 
like a denial into the matter. You cannot obtain a denial 
out of a pure privation, i. e. a mere profession of ignorance, 
but then in view of the positive mass and far-reaching pre- 
sumptions of knowledge as a whole, no privation however 
complete 1 - can be quite pure 1 , i.e. quite free from positive 
grounds of denial. A complete and persistent privation 
must always, as I have tried to show above, verge upon an 
exclusion. But if we had at command a direct and positive 
ground of denial, then I imagine that we should not restrict 
ourselves to refusing to state the chances, i. e. to %, but 
should employ the symbol o. Or, in order to indicate 
that a case has no chances in its favour because all the 
possible chances are absorbed by another case which is 
certain and which excludes the former, we ought I should 
think to use the expression , i. e. negation grounded in 

1 By a 'complete' privation I mean one in which we know absolutely 
nothing in favour of the matter of which we deny all knowledge, while I call 
a privation ' pure ' in as far as we know nothing positive against the matter of 
which we deny all knowledge. And my suggestion is that, looking at know- 
ledge as it really exists, wherever we have the former case it is almost impossible 
to have the latter. 

376 Disjunction and the statement of Chances. 


positive certainty, which is the remainder of -f- and so 
represents the total certainty available for the two cases as 
entirely absorbed by the one. Thus we should have three 
symbols representing ideas which we ought not to confuse, 
for demonstrable impossibility, % for absolute ignorance 
(privation alike of real possibility and of impossibility), \ for 
a conflict of proofs, such that truth and falsehood are equally 
grounded alternatives, which in presence of absolute igno- 
rance is not the case. 

^ *Vti*vv ff ft**v*f&y'**4s 



I. I PROPOSE to conclude the discussion of the judgment Kant'sview 
with a short treatment of Modality. For Modality, if it mentally 
exists at all, is simply the degree in which individual judg- J ust - 
ments participate in the certainty of that permanent and 
all-embracing judgment by which the individual intelligence 
sustains those qualifications of the Real which for it consti- 
tute Reality. Our account of Modality must therefore 
resolve itself into a recapitulation of the principal types of 
judgment, having for its object to bring together in a single 
view certain of their characteristics which have already 
been noticed. The question before us is whether and in 
what sense there are degrees of logical certainty ; not 
merely of habitual conviction, or of readiness to act on a 
belief, which are psychological and not logical, but of that 
characteristic which forms the differentia of judgment, and 
which may be described as logical assertiveness. This 
logical assertiveness itself indeed includes a psychical or 
psychological element which must be carefully distinguished 
from the purely logical or rational element of assertiveness. 

One preliminary difficulty meets us on two sides. We 
find Kant 1 maintaining that modality affects only the 
copula in judgment, and that therefore, though a measure 
of assertiveness, it is indifferent to the content affirmed. 
And we find it maintained against Kant that modality has 
no reference to the copula in judgment, nor, consequently, 
to the assertiveness of assertion, but is a peculiarity of the 

1 Kant, Kritik der r. V. p. 97 (Hartenstein), ' Von der log. Function im 

378 Modality. [Booki. 

content affirmed which does not affect the essential act of 
affirmation 1 . Both of these views, it will be remarked, by 
separating the assertiveness of assertion from the content 
asserted, represent judgment as an arbitrary and irrational 
activity. It is not surprising that in the ' Grammar of 
Assent' ecclesiastical interest should have thrown itself 
zealously on the side of such a conception. 

The view which I have attempted to explain in the 
present discussion is incompatible with both of the above- 
mentioned ideas. Every judgment, as we have seen, unites 
in it two elements of certainty ; the formal or psychological 
element, which consists in a reference of its content in virtue 
of a perceived identity to the individual's personal world of 
perception and experience, and the material or logical 
element, which consists in the attachment of this content 
by rational necessity to the organised nature which the 
Real possesses as already qualified by the individual's 
knowledge. The former element corresponds to memory 
and the latter to reasoning. All reasoning is in the medium 
of memory, but memory as such does not involve reasoning. 
The two activities however are one in origin and in ultimate 

Now the psychological element of certainty does not 
vary. The unity of a content with the individual per- 
ceptive self admits of no degrees. If it appears to vary in 
degree, we are remembering by something, i. e. we are eking 
out memory by reasoning. Memory as such is dumb in 
presence of questions or comparison of grounds. It tells us 
nothing beyond the mere content which it recalls. But 
material or logical certainty depends on reasoning, and is 

1 Sigwart and Bradley certainly agree in this. Lotze seems to say it of the 
old Modality, in which ' It must be so counted as apodeictic,' but does not 
distinctly say it of Modality as understood by himself (and subsequently by the 
other moderns above mentioned), which requires hypothetical or disjunctive 
form for apodeictic judgment. In his suggestion as to Modality Lotze was of 
course anticipated by Hegel. Sigwart and Bradley deny the superior logical 
certainty of the apodeictic judgment, and Sigwart even disparages it on the 
ground of its mediate character. Here, at any rate, he commits a gross blunder. 

chap, ix.] Kant on Problematic Judgments. 379 

therefore capable of more and less, and is the chief element 
of the assertiveness of judgments. It follows that modality 
is, as Kant said it was not, a characteristic of the content 
affirmed, but is also, for that very reason, as the moderns 
say it is not, a. measure of the assertiveness of assertion. 
Whether modality must be said to affect the ' copula ' at 
all, or the copula only, depends on what we mean by the 
copula. If the copula is formal and empty, an unexplained 
act of reference like that of memory, then modality does not 
affect it, or rather it does not affect modality. If, on the 
contrary, the copula is the act by which grounded necessity 
is recognised, then it is the essence of modality. The 
formal and indifferent copula of traditional logic is the 
psychological copula, and when treated as the logical 
copula becomes a logical copula indifferent to the logical 
content 1 , which is absurd. 

As a matter of organic principle, therefore, I shall follow 
Kant, although by what I must regard as a confusion, he 
refers modality to the form of judgment and not to the 
content, and although his 'problematic judgment ' is rightly 
pronounced by later writers to be no judgment at all. His 
summary runs thus : ' Because, then, in this aspect [i. e. in 
modality] everything incorporates itself with the intelli- 
gence by degrees, so that one begins by judging pro- 
blematically, and subsequently takes the matter to be 
true assertorically, and ultimately affirms it as inseparably 
united with the intelligence, i. e. as necessary and apodeictic, 
it follows that we may confer on the three functions of 
modality the further appellation of so many moments of 
thought as such 2 .' Here as throughout philosophy it has 

1 Lotze does not fall into this trap. But he seems only to avoid it at the 
cost of separating off a particular fragment of content to be identified with the 
copula, at least when he is explaining the traditional view. But as against 
this the traditional view was right. The copula must have to do with all of the 
content or with none. In Lotze's own view of Apodeictic Judgment it has to 
do with all. 

2 Nearly equivalent to what I have often spoken of as non-impossibility. 
See below. 

380 Modality. [Book i. 

been the task of later writers to realise in the concrete a 
conception enunciated by Kant, but by him only half 
liberated from the formulae of obsolete conventions. 
Hegel's analysis of the hypothetical and disjunctive judg- 
ment, adopted by Lotze and subsequent writers, is the 
realisation of Kant's idea of modality as progressive incor- 
poration with the understanding. 
The Pro- 2. In order to begin at the beginning we must start from 
Tndgment. Kant's 'problematic' judgment, which, as he describes it, 
is not a judgment at all. The problematic judgment 
according to him expresses mere logical possibility 1 , not 
' objective ' possibility, and he gives as examples of it the 
antecedent and consequent in hypothetical judgments, or 
the isolated members of a disjunction. 
Nature of i. But such elements of thought are of course by them- 
or (fues- 0n se ^ v ^ s not judgments, i.e. as Kant himself says, they are 
tion. not assertory. It may be doubted however whether such 

elements of thought exist by themselves at all, and whether 
they do not of necessity enter into some judgments. Their 
nature is no doubt the same as that of the genuine 2 Ques- 
tion, which Sigwart has the merit of having discussed. I 
cannot think however that his psychological expressions 
help us to grasp the logical differentia of question or doubt. 
It is nothing to say that the idea merely floats 3 before the 
mind. It must, in order to rank as a definite doubt or 

1 Kritik der r. Vernunft, p. 97 (Hartenstein's ed.). 

2 The question which expresses a real doubt or ignorance ; not one to which 
we know the answer, but ask in order to force the interlocutor to give it. This 
latter is an imperative, as Sigwart says (vol. i. 190-1). But then the former 
hardly perhaps has the differentia of the Question, which is just this imperative 
significance. So the ' genuine ' Question is perhaps not a Question at all, but 
only a state of knowledge. What state of knowledge ? Obviously one that 
presses for an advance, so probably a disjunction of ignorance. Kant's proble- 
matic judgment includes all supposition qua supposition, although known to be 
false or known to be true. But I do not think that Sigwart's complaint of a want 
of distinction between these cases and that of genuine doubt is well founded, 
because a supposition qua supposition is considered by an act of abstraction 
apart from the relations which constitute its falsity or certainty. Therefore, as 
subject to this abstraction, any supposition may rank as a doubtful judgment. 

3 ' In der Schwebe.' 

chap, ix.] 'Floating Ideas! 381 

question, make some specific claim, be a candidate for some 
definite place, in the permanent judgment of consciousness. 
There is a nearer approach to something intelligible in the 
suggestion that a problematic judgment is a judgment about 
oneself, saying that in the matter before us we are unable 
to judge. But this, though often true in fact, is an eva- 
sion of the theoretical difficulty. There must be some 
definite logical situation in virtue of which we say this. 
When we judge that a judgment is merely possible we 
must judge that its content has mere possibility. The 
reduction of judgment of possibility to possibility of judg- 
ment is an attempt to take refuge in psychology from a 
logical difficulty. 

Although then the mere idea of a judgment, floating be- 
fore the mind, is not, even if it exists, a judgment at all and 
therefore not a problematic judgment, yet every genuine 
question and every judgment made subject to a ' possibly ' 
or 'perhaps' represents a peculiar logical situation, and 
not merely a psychological incompleteness of the act of 
judgment. It is not true as a rule that we begin with 
floating ideas and advance from them to judgments. I 
doubt if such a beginning is possible ; it is certainly not 
normal. Our thought consists in the continuous modifica- 
tion of judgments I had almost said, of a single judgment. 
The question, considered as a state of knowledge, is a dis- 
junctive or hypothetical judgment used as the premise of an 
inference. A groundless question is as unreal as the ' in- 
finite' judgment. I cannot ask 'Are you going home?' 
except on the basis 'You are possibly or probably going 
home,' which means when analysed either ' If x is the case 
you are going home,' or else ' Either you are going home, 
or x is the case.' The question does not mean c I have a 
floating idea in my head of you as going home \ and want 
to know if I am to refer this to reality.' It means rather, 
' I judge true of reality a definite situation in which some 

1 The idea is not ' of you as going home ' but ' that you may be going home ;' 
i. e. something is judged, which may result in your going. 

382 Modality. [bookI. 

conditions of your going home are included ; I want to 
qualify reality by this situation more precisely defined ' or 
to qualify a further element of Reality, viz. yourself, by it. 
Thus Kant is not so far wrong in identifying a problematic 
judgment, or, as we may call it, a genuine question, with an 
isolated member of a complex enunciation ; but it is only 
as a corollary from the complex thought or as an inability 
to make its outline precise, and not as a mere isolated 
member of it, that the problematic expression can be a 
judgment at all. For in its isolation, ex hypothesis it is not 
referred to reality. 
Problema- ii. Possibility, then, as Mr. Bradley has told us, is a 
Apodeictic species of necessity, and it seems to follow from this that 
Judgment, the problematic judgment is a form of the apodeictic judg- 
ment, and that any series of gradations in which the two 
have, separate places such gradations as Kant laid down 
must be in contradiction with the nature of the case. If 
the judgment of possibility is the first form under which 
matters of knowledge attach themselves to the under- 
standing, then it can hardly be a species of the final form, 
and ought to be verifiable in early thought. 

We must begin by admitting the difficulty indicated by 
the last objection. All judgment, I have said, is in one 
respect assertory. It is probable that very early thought 
may present no other aspect. The distinction between 
memory and intelligence is a late distinction. The old 
man in Homer * who ' knows ten thousand things ' cannot 
but remind us of the schoolboy whose friend ; knows an 
awful lot.' Whatever is in the mind, such expressions 
seem to suggest, ranks alike as knowledge. The assevera- 
tion, indeed, may be supposed to begin as soon as man feels 
the danger of deceit ; and this form of speech recognises a 
distinction in degrees of certainty, and attempts to raise 
one matter of knowledge to the standard of another. But 

1 Homer is of course not primitive, but poetry is very conservative, and 
Homer is full of ideas which are derived from very early strata in the 
mind's formation. 

chap, ix.] Possibility and Necessity. 383 

on the whole, the distinction between memory and intelli- 
gence, and therefore that between mere reference to per- 
ceived reality and systematically grounded insight, would 
probably be found a vanishing distinction if we could 
examine the earliest phases of the human mind. Possi- 
bility, mere assertion, and necessity, as they exist for the 
civilised mind, are based upon differences that concern the 
material logical or systematic element in judgment. We 
have to remember however that logical facts exist long 
before the technical names for them, and we must not limit 
the existence of modalities by that of words like possibility 
and necessity, but only by that of speech-elements bearing 
the power of ' may,' ' must,' ' shall,' or c would that.' And 
we must add that we cannot see how judgment should 
exist apart from all sense of rational necessity. A mere 
instinctive identification with reality, wholly without why 
or wherefore, is rather a theoretical limit below which 
judgment cannot be taken to exist, than an historical phase 
of the judging faculty. 

The next difficulty is that possibility appears on the 
view taken above to be a species of necessity, and yet to be 
prior to necessity. In order to explain this we must refer 
back to the doctrine of opposition and conversion. Strictly 
and properly, a judgment can only be denied by another 
judgment of the same nature; a singular by a singular 
judgment, a generic by a generic, or a hypothetical by a 
hypothetical. But a very strong implication of denial can 
be conveyed by a judgment which being of a different type 
from that contradicted denies the right of this latter judg- 
ment to the type which it has assumed. If, however, the 
denial is to be prosecuted in earnest, the judgment of the 
lower type must be capable of maintaining itself on the 
level of that which it assails. Possibility, if not derivative 
or calculated, represents such a first effort at denial, directed 
against a necessary judgment, and may or may not go on 
to assume an explicitly necessary form. 

a. Thus possibility as prior to necessity follows the 

384 Modality. [book i. 

Particular meanings and development of the Modal Particular, which, 
ju gmen . QW - to t ke continuity in the evolution of thought, on 

Exception r . . . . . i- * . 

and in- which we have so often insisted, has its roots far back in the 
stance. quasi-singular or particular enumerative judgment. That 
is to say, the consciousness of possibility begins I do not 
mean in every case, but in its most rudimentary logical 
form with a rule and an exception or with a positive in- 
stance suggesting a rule. And it passes into a further type 
with the essentially negative, or again with the essentially 
positive modal particular. The latter, indeed, the positive 
modal particular, is hardly intelligible apart from the 
explicit recognition of necessity. But in accordance with 
a principle to which we shall have to recur it is quite cus- 
tomary for thought to employ a derivative and secondary 
judgment which is dependent upon a primary principle 
remembered as a rule. Many judgments of possibility 
those current in systematic thought are after this fashion 
corollaries from judgments of neccesity, or rather from the 
fact that certain judgments of necessity are accepted as 
true. I now proceed to illustrate the development just 

Possibility is at first negative. Bare negation indeed is 
nothing, but possibility in its simplest case comes very near 
bare negation. Such a possibility when veiled under the 
equivocal form of the particular judgment rests on an 
exception. We must not suppose that the possibility is 
positive because the exception is a positive case. The con- 
tent of a mere exception as related to the rule which it 
impeaches is purely negative, i. e. only contradicts, and sug- 
gests no contrary principle. Suppose we have a half- 
collective and half-generic judgment like 'All English rail- 
ways are well managed.' Suppose that then we come 
upon an English railway which is not well managed, and 
embody our observation in the judgment 'There is an Eng- 
lish railway which is not well managed.' This may readily 
be interpreted as a judgment of negative possibility, 
amounting to no more than this, ' It is not true that 

chap, ix.] Degrees of Possibility. 385 

English railways are in every case well managed,' or in 
other words, ' It is not impossible for an English railway to 
be other than well managed.' The principle is just the 
same if the rule is negative, e.g. ' No crows are white.' An 
exception would contradict this, but only by establishing 
little more than mere possibility (not-impossibility) that 
a crow may be white. ' There is a case in which a crow is 
white ; ' ' It is not true that no crows are white.' 

The instance makes the step from negative to positive 
possibility. Like the exception, it implies a generalisation, 
at least incipient, but it supports this generalisation instead 
of contradicting it. Supposing, what is always ultimately 
the case, that the exception is a latent instance, the judg- 
ment which expresses the exception will change, in coming 
to express an instance, from a mere contradictory to a con- 
trary which is also contradictory. Let the original rule be 
1 No secular education can be spiritual ' and the exception 
be ' In the case of literary education we have a secular 
education which is spiritual,' with the negative result ' It is 
not true that no secular education can be spiritual.' Then 
when we go on to treat the exception as an instance 1 we 
get a result hardly differing from the former in words, but 
charged with the material distinction that we now see 
reason to think that 'secular education as such may also be 
spiritual/ i.e. It is possible that or 'There is real ground 
for supposing that secular education, etc. etc' 

(3. When we advance to the modal particular we have Negative 
the same distinction in a purer form. The modal particular Positive 
has been treated above as the converse by limitation 2 of a Possibility. 
hypothetical judgment, and at all events may always be 

1 Exception presupposes rule, and rule presupposes positive instance, it may- 
be said, so that our idea of negative possibility coming first gets us into a 
circle. The fact alleged is true ; a positive rule must come from somewhere, 
and probably from a positive instance. But prior to the idea of denying the 
rule the generalisation is direct or naive, and does not pass through the stages 
of modality except on the embryo scale on which it also implies negation. 

If the hypothetical judgment has a negative consequent, it is of course need- 
less to limit it in converting. 

VOL. I. C C 

386 Modality. [booki. 

treated as the contradictory of another hypothetical judg- 
ment. ' If A is B it is C ' becomes when converted by 
limitation * If A is C it may be B,' which latter is at least 
the contradictory of ' If A is C it is not B.' Where the 
modal particular really originates by the conversion of a 
hypothetical judgment, it is of course an inference or corol- 
lary from a principle with reference to another and oppo- 
site principle. But as usual the actual or historical modes 
of initiation of the judgment are one thing, and its logical 
essence another. Obviously the modal particular may be 
generated either by inference from explicit principles, or by 
the suggestion of rules through instances. 

In any case the judgments 'A may possibly be B' and 
1 A may possibly not be B ' have two degrees of meaning 
analogous to those of the exception and the instance. 
They may be mere contradictories of the hypothetical 
judgment to which they are respectively opposed, or they 
may be contradictories growing into contraries. If they 
are mere contradictories, corresponding to exceptions, then 
the judgment 'A may be B' merely means to overthrow 
the principle that 'A cannot be B ' ; that is to say it asserts 
that if or though A is, yet it does not follow, from that, that 
B is not. It is easy to give the corresponding significance 
to ' A may not be B.' But precisely the same judgments 
* A may be B ' and ' A may not be B ' are capable of cor- 
responding to the instance, and their meaning then is that 
there is some positive connection between an unspecified 
condition x, which is fairly conceivable of A, and B or the 
negation of B as may happen. Under these circumstances, 
even though we do not know that Ax itself is actually 
found in experience, yet we have ground for saying that 
there is a rational connection or antagonism between A 
and B. Many degrees of these connections are to be met 
with. If x were the entire ground of B, and we knew x to 
be true of A, then we should no longer have possibility but 
certainty. But if x is part of the ground of B, and we know 
x to be true of A, then we have a degree of real possibility 

chap, ix.] Meanings of Possibility. 387 

varying with the relation of x to B. Or again, if x is not 
the ground but a consequent of B, and we know categori- 
cally that A is x, we have in effect an inference, from the 
hypothetical ' If A is B it is x' converted by limitation 
into ' If A is x it may be B.' I will give a concrete 

Plants (A) may possibly possess sentience (B). Taken 
as the mere guess of an unscientific mind prepared to say 
the same no less of stones and metals, air or water such a 
judgment would represent a mere negative possibility, or in 
other words, it would express no more than the fact that 
having considered the universal judgment ' Plants are not 
sentient' the individual mind happens to see in it no se- 
quence of reason and consequent and therefore pronounces 
that ' There is no ground for asserting that plants are not 

But the same judgment ' Plants (A) may possibly have 
sentience (B) ' is capable of conveying a more positive 
meaning. It may rest on the conviction that ' If plants (A) 
have irritability (x) they must have sentience (B).' Assuming 
ignorance as to actual observations of irritability in plants 
we nevertheless have then a certain congruity 1 to go upon 
in saying that A may, in a sense that has a certain basis of 
reality, be B. But still more strongly, if we could say 'If 
Plants (A) have sentience (B) they must have irritability 
(x)S being able to supplement this with the fact ' There are 
plants (A) which have irritability (x),' we should be able to 
affirm 'There are positive grounds for maintaining that 
plants A have sentience B.' 

Possibility may therefore mean (i) the inability to make 
a certain hypothetical judgment, so long as we bear in 
mind that mere privation or inability is a limit which the 
judgment must not actually reach if it is to retain signi- 

1 We should not e. g. attach any such weight to the judgment that if a 
plant had poetic genius it must have sentience. I claim throughout that con- 
gruity is essential and not accidental in supposition. If we go outside the system 
of fact which is our basis of supposal, we get results analogous to the ' infinite 


388 Modality. [bookI. 

ficance. This possibility is non-impossibility. Or it may 
mean (ii) the inference from a hypothetical judgment, 
whether explicit or suggested in instances, which (a) assigns 
an intelligible condition (or makes us believe that there is 
such a condition), which would if real establish the conse- 
quent whose possibility, assuming the reality of the sub- 
ject of judgment, is in question, or (b) assigns a certain 
logical consequent to the attribute or event in question 
considered as a logical antecedent, which consequent is 
known to be real. This logical consequent may be either 
an effect with alternative causes, or a consequent with alter- 
native reasons. The ideal or reciprocal form of the hypo- 
thetical judgment excludes mere possibility and therefore 
does not concern us here. 
Essence y. It is plain from the above examples that the terms 

Hematic " ' possible,' ' probable,' ' may,' * might,' and ' must,' stand for 
Judgment, more or less reflective estimates of certain kinds of knowledge. 
The essence of the problematic judgment is the substi- 
tution of such an estimate for the concrete steps of in- 
ference really involved in an affirmation. Possibility 
results in referring to reality, without transition, but subject 
to an estimate, what is only connected with it by transitions. 
When the whole transition is made explicit, the allegation 
of possibility is superseded 1 . The judgment which has all 
its conditions and reservations fully assigned to it is of 
the apodeictic order ; possibility arises from effecting the 
reference to reality apart from the conditions. The idea 
of ' possibility ' is our substitute for the omitted conditions. 
Obviously such an idea may emanate from all degrees of 
confused perception or of reflection. We may be silent 
about the conditions either because we cannot clearly grasp 
them, or because we are explicitly abstracting from them. 
But an estimated indirectness of transition there must be if 
we are to judge problematically. Disjunction can be 
treated in the same way, owing to the hypothetical inter- 
relations of its members, and thus the statement of chances 

1 Cp. p. 360, supra. 

chap, ix.] Assertory Judgment. 389 

is a clear and extreme case of the estimate in question. Its 
essence is to burden the reference to reality of one alterna- 
tive with a hindrance drawn from the number of other 
alternatives. All. possibility indicates a similar tendency. 
But the statement of chances has measured its own cloudi- 
ness and made certain of its own uncertainty \ It is there- 
fore no longer problematical. It supplies a definite predi- 
cation of a hindrance to reality, and not a hindrance to 

Thus the true problematic judgment is a judgment with 
a peculiar and reflective content, which interferes with its 
assertiveness. It is a hypothetical or disjunctive judgment 
in disguise. All judgment whatever is within a real system, 
but the problematic judgment has its relations to its real 
system peculiarly obscured or neglected. In the question, 
for instance, we only make explicit a part of the intel- 
lectual state, ultimately affirmative, on which our desire for 
further knowledge depends. A question indeed often 
vanishes when we insist on its being clearly put. 

3. The other forms of modality may be briefly dismissed. Assertory 
Every judgment may be called assertory, as we saw, in virtue smen 
of its psychological reference to self- feeling. If any judgments 
are to be called assertory in a strictly logical and material 
sense, they must of course be the singular judgments which 
depend on union of attributes within the concrete subject 
of the judgment, and not on their necessary connection in 
a larger subject falling outside the judgment. Such judg- 
ments are even logically assertory in as far as the concrete 
subject is merely individual as a synthesis of differences not 
connected by abstract necessity. So far on the other hand 
as it displays individual character and lends itself to analo- 
gical affirmation, it stands for the present purpose on the 

1 This is the reason why the ' Thermometer of Probability ' (see De Morgan, 
Budget of Paradoxes, p. 416) would not be of very general application. What 
it measures is the ratio of the whole number of equal alternatives arising on a 
certain condition to the number of desired alternatives so arising. But in con- 
crete knowledge we have no security of finding equal alternatives. 

390 Modality, [book i. 

same footing with the subjects of necessary and apodeictic 
judgments. The assertory judgment has a higher degree 
of assertiveness than the problematical judgment as such, 
because its reference to reality though not apodeictic is 
direct and open. It would be impossible to maintain 
Kant's view of a progressive incorporation of contents with 
the understanding, if he meant that every trivial judgment, 
say, of perception, was preceded by a recognition and 
estimate of uncertainty. But all experience supports his 
contention that imperfect judgments in which only one 
element is clear, and in which this clear element is attached 
to reality through others which are not clear, belong to a 
less complete phase of knowledge than judgments in which 
the reference is clear and complete. If the problematic 
judgment arises by intentional abstraction from precise 
knowledge, this makes no difference. We are returning on 
purpose to an imperfect form of judgment from a more 
perfect one, in order to exhibit a net result which the more 
explicit form will not display. We must stand by the 
result which we thus obtain. We cannot eat our cake and 
have it. 

Of course where an instance indicates a possibility, the 
assertory affirmation of the instance and the problematic 
affirmation of the possibility do not refer to the same con- 
tent. ' This Drosera shows irritability ' is a singular judg- 
ment of perception. The problematic judgment 'There 
are conditions though unknown in detail under which the 
nature of a plant develops irritability,' i. e. ' A plant as such 
may have irritability ' arises from the analysis of the above 
instance into a general suggestion. Such an analysis is 
probably concurrent with the perception of individual 
identity on which the Singular judgment rests, but the two 
are not identical. Imperfect insight into necessary con- 
nection may affect the same content which is being erected 
into a thing, but is not one with this process of erection. 
Assertory assertion and problematic assertion may be and 
must be conjoined in every problematic judgment, but they 

chap, ix.] Elements of Uncertainty. 391 

refer to different elements in the content affirmed, the 
former to the system as a concrete real whole, the latter 
to some element of the system as related by abstraction to 
the other elements. When the latter aspect of the judg- 
ment is dropped or superseded we have the assertory 
affirmation pure and simple. The assertory judgment has 
no degrees of assertiveness except in so far as in virtue of 
its specific content the problematic or apodeictic judgments 
inevitably show themselves within it. 

4. Judgments of apodeictic character, i. e. hypothetical The Apo- 
and disjunctive judgments, lay claim in virtue of their form judgment. 
to a higher degree of assertiveness than either problematic 
or assertory judgments. The reason of this is that their 
form has for its differentia the exact exposition of the 
transitions, conditions, or alternatives subject to which the 
judgment is true of reality. By such exact exposition the 
content either becomes an articulated system, or at least 
reveals itself as fitted to take a place in such a system. 
The former is the ideal of the disjunctive, the latter that of 
the hypothetical judgment. Reality considered as abso- 
lutely known is of course ex hypothesi taken to be abso- 
lutely asserted. But Reality is not by any sane person 
considered to be absolutely, i. e. completely and precisely 
known. Degrees of certainty in apodeictic affirmation arise 
from the consciousness a logical consciousness made ex- 
plicit in the structure of judgments that the individual's 
knowledge is but imperfectly identified with the ideal 
judgment which would qualify Reality by the complete 
content of Reality. 

i. In the hypothetical judgment, as we have seen, though The Hypo- 
/r jo thetical 

important elements are made explicit, yet the connection judgment. 

which is affirmed implies an underlying reality which is not 
expressed in the content of the judgment. Therefore the 
hypothetical judgment is subject to two elements of uncer- 
tainty, viz. its own reference to the limited reality the affir- 
mation of which it implies, a reference which may be 
partial or confused, and further the relation of that affirmed 

392 Mo da lity. [book i . 

real system to the content of Reality as a whole. ' The 
British Parliament is able to alter a statute affecting its 
own duration.' This is rather a generic than a hypo- 
thetical judgment ; but for the present purpose these two 
types must rank as very closely akin. About such a judg- 
ment there is first the question whether it really follows, or 
how necessarily it follows, from the facts which we are pre- 
pared to affirm of the reality known as the British Consti- 
tution, and secondly, what opening these facts themselves, 
as compared with the greater reality of our entire ex- 
perience on the ground of which they in turn are affirmed, 
leave for error or for unseen modification. Any disjunc- 
tive judgment, as compared * with a given hypothetical 
judgment of which it may be regarded as a development, 
makes this underlying real system explicit, and therefore 
has no source of uncertainty but that of a failure in the 
necessity by which this system itself is attached to Reality as 
a whole. But of course the disjunctions which we commonly 
use are for the most part systems within known systems, 
and therefore stand on the same logical level of certainty 
with hypothetical judgments. Such e.g. is the disjunction 
which expresses the number and nature of the conic sec- 
tion, resting as it does on the ultimate real system which 
we take to be the nature of space. Only disjunctions that 
embody a complete and coherent sphere of knowledge, 
such e. g. as the nature of space, have the character which 
has just been ascribed to the ideal disjunction. But even 
with such a disjunction we still have the difficulty in the 
background, ' Does the real system which we affirm ' in 
this example the nature of space ' really emanate as a 

1 It is absolutely necessary when we attempt to compare judgment forms 
in respect of their essential import, to select instances which belong to one 
and the same progression. A hypothetical judgment drawn from an advanced 
phase of science has at once more content and more precision that a disjunctive 
judgment drawn from everyday experience. To judge the capacities of the two 
forms by instances so selected would be like judging the powers of civilisation 
and savagery by comparing a civilised infant without allowance for age to an 
adult savage. 

chap, ix.] Degrees of Apodeictic Assertion. 393 

necessity of knowledge from the whole reality which is 
forced upon us by experience?' It appears to me to be 
quite idle to maintain that all judgments, or even that all 
necessary or apodeictic judgments, are on a level in this 
respect. Ultimately, we may imagine, nothing can be 
rightly known without knowing all else rightly, so that 
every isolated fact and principle of knowledge would be 
implied in, say, the existence of morality or in the existence 
of an intellectual world. But as knowledge is in fact con- 
stituted its parts are fragmentary and incoherent, and there 
is much that we affirm upon only a partial or limited neces- 
sity, while much again is so incorporated with the whole 
fabric of our real world that we feel bound to maintain 
the former if we would not fall into hopeless contradiction 
with the latter 1 . The assertiveness of affirmation is not 
indeed measurable outside the calculus, but it is capable of 
being perceived and to some extent compared. It is not a 
mere feeling, but an insight into connections. It is absurd 
to maintain that in affirming the whereabouts of a friend, 
or the harmonious or other effect of a combination of 
colours, or the continuity or non-continuity of matter or of 
space, I am pledging my intellectual existence to the same 
degree as when I affirm the relations of the multiplication 
table, or (subject to the requisite interpretations) the law 
of causation, or the existence of moral purposes. 

The uncertainty which may attach to apodeictic judg- 
ments arises then from the same cause as the uncertainty 
of problematic judgments, but the cause is operative in a 
different mode and in a slighter degree. We always feel 
certain when we judge, for all judgments involve the same 
psychological identification with self-feeling. But we know 
that this certainty is conditional on our expressing Reality 

1 This must be read subject to reservation as regards the actual language in 
which abstract principles are expressed. It is a recognisable function of the 
body of knowledge, not a limited set of stereotyped ideas, which we may be 
justified in holding indispensably necessary to our reason. See below, Bk. II. 
chap. vii. 

394 Modality. [book i. 

with precision and completeness, and this we are well aware 
that we never do. Of course, to begin with, the apodeictic 
form of judgment is no guarantee, any more than any other, 
against falsehood or frivolity. There may be no under- 
lying real system at all, or that which is taken to be referred 
to may in no way justify the sequence erected on it. Any 
false generalisation is an instance of this. Or again, the 
necessary transition may be quite incompletely set forth, so 
that the judgment sinks ipso facto into a problematic judg- 
ment in spite of its apodeictic form. Such are judgments 
in which a remote cause or consequence taken as a sign is 
substituted for the ground of the sequence, so that the 
judgment though not untrue in fact has the appearance of 
a riddle. ' If the stick will beat the dog the old woman 
will get home to-night' Here we have no indication of the 
real arrangement on which the sequence rests, and the con- 
dition, so far as can be seen without copious supplementa- 
tion from ulterior knowledge, is irrelevant and equivalent 
to an unknown condition, implying as it does a number of 
unknown conditions. This is the explanation of the exam- 
ples to which Sigwart appeals as showing that apodeictic 
judgments are not in fact made with any peculiar certainty 
of conviction. ' There is a common idea that the apo- 
deictic judgment stands for something higher than the 
assertorical. It is believed that if we start from the pro- 
blematic judgment and ascend to the apodeictic we steadily 
increase the certainty of our knowledge, and add to the 
worth and dignity of our assertions. This idea must be re- 
linquished. All mediate certainty must stand in the end 
on immediate knowledge ; the ultimate premises of every 
proof cannot be proved. The usages of life stand in comic 
discrepancy with the emphasis we lay upon apodeictic cer- 
tainty. The sayings " It must be so," " It must have so 
happened " are judgments apodeictic ; but the confidence 
they express has most modest limits V 

This is not the place to criticise the fundamental view 

1 Sigwart, Logik, i. 195, quoted in Bradley's Principles of Logic, p. 186. 

chap, ix.] Degrees of Apod eic tic Assertion. 395 

which Sigwart here expresses, but to which he is, happily, 
not faithful throughout. In treating explicitly of the 
nature and bases of inference we shall see that the distinc- 
tion between mediate and immediate knowledge coincides 
with the distinction between what is known and what is 
only on the way to be known. If Sigwart meant what he 
said in this place, he would have cut himself off from all 
possibility of believing in science. As to the examples 
which he adduces, they fall into their place, according to 
what has been said, as problematic judgments. ' It must 
have so happened ' is an inference from reality under a 
condition, to reality without an expressed condition, and 
therefore is problematic. 

The degrees of certainty belonging to the apodeictic 
judgment itself are as we saw of the same kind as those 
which characterise the problematic judgment. The whole 
of the reality on which the sequence is intended to be based 
may not have been brought to bear upon the sequence, and 
even if it has, its own relation to the reality which is the 
ideal of knowledge may be so disproportionately trifling as 
to make the judgment an especially inadequate embodiment 
of the ideal Reality which alone is certain. 

I may illustrate this conception by our present know- 
ledge of Hypnotic and kindred phenomena \ The curative 
action of Hypnotism, or the beneficent anaesthesia which 
may be produced in some forms of the Hypnotic state, are 
now as it seems matters capable of embodiment in empirical 
generalisations. These rules or laws can be exhibited, like 
all rules or laws, in hypothetical or disjunctive form ; that is 
to say, as consequents following upon conditions, or as 
alternatives arising within a certain identical content. On 
a certain degree and kind of hypnotic trance a certain 

1 I believe myself justified, when writing for purely logical purposes, in 
treating the actual phenomena known to science as freely as may be necessary 
to give them sharp outlines, and to avoid a mass of reservations and qualifica- 
tions that would be only an encumbrance for my present purpose. I on my 
side hope to keep clear of wilful distortion, but the reader on his side must not 
accept my illustrations as citations from a biological text-book. 

396 Modality. [book i. 

anaesthesia is consequent. A hypnotised subject is capable 
of some three or four recognisable alternative states. In 
certain forms of nervous derangement acquired, or, as it 
seems, congenital, repeated hypnotic treatment exercises a 
sanative influence. 

Now although I personally entertain no doubt that 
there is, as the phrase goes, 'something in' all these con- 
ceptions, and though I am prepared to affirm them, i.e. to 
judge them true of reality, as embodiments of an ex- 
perienced content which must be affirmed somehow and 
which I cannot affirm otherwise, yet so far as I understand 
myself I do not stake my intellectual existence upon them 
as I do on the existence of causation, or morality, or 
beauty. On what I mean to say in them, on the ex- 
perienced content from which they are drawn, I do stake 
my intellectual existence ; but this content, apart from my 
explicit judgment, is to me an x, a thing- in-itself, a nothing. 
I must stand or fall by my judgment as it is, not merely 
by my ultimate intention to embody reality, which is the 
common and formal feature of all affirmation. And I know 
perfectly well that by my explicit judgment on such mat- 
ters as these I am very likely to fall. The reason of this is 
not that the cases on which I rely are few in number, 
compared, e. g. with ordinary cases of the operation of digi- 
talis on the heart or of mercury on the liver. One case is 
enough, as we all know, where the framework of knowledge 
stands ready to receive it with the grip of necessity. The 
reason is rather that the organised system of reality within 
which the sequences in question have their force, lies or 
has hitherto lain outside the great fabric even of biological 
science, not to speak either of deductive reasoning on the 
one hand or of philosophical construction on the other, 
been as a whole identifiable either with the principles of 
The principles of abnormal psychical phenomena have not 
physical causation or with those of normal psychical de- 
velopment. The judgment is therefore obstructed by the 
want of contact or necessary relation between the system of 

chap, ix.] Hypothetical Disjunction. 397 

such abnormal phenomena, which it must in some way refer 
to reality, and the entire cosmos of normal evolution. Sup- 
posing, however (I speak merely by way of illustration), 
that the abnormal states in question, even those which pre- 
sent the apparent puzzle of a morbid origin combined with 
a curative effect, could be exhibited as cases under the 
known principles of evolution, the whole ground and cer- 
tainty of the judgments relating to them would be put 
upon a new foundation. It is an old idea 1 that many 
states and susceptibilities of the soul, which are commonly 
treated as mere freaks of nature or capricious results of 
disease, may really have their place among the phenomena 
of evolution no less than sleep and waking, or the one- 
ness, expressing itself through heredity, of parent and 
child. If peculiar forms of sensitiveness and peculiar 
' morbid ' states or transitions to states could be brought 
under such heads as survival, reversion, or analogous de- 
velopment, their underlying reality would be grafted on the 
main stem of the organised real world, and the necessity 
with which they were affirmed would become more deter- 
minate and more concrete. 

ii. Disjunction by its form aims at the standard of a The Dis- 
complete and therefore of a real system. 'Real ' because it T^^ent. 
points to nothing beyond itself as an implied ground of 
truth. We have seen sufficiently above that no objection 
can be raised against the reality of the content of any judg- 
ment by reason of its being extended in space or time. 
No judgment confines its reference within an atomic ' now,' 
and no reality can display itself as existent within an 
atomic now. It is grammatically possible however for 
a disjunctive proposition to express a judgment which is 
hypothetically disjunctive : l A man who would act so must 
be a knave or a fool.' This shares the character of all 
hypothetical judgments in implying an unexpressed real 
system as the basis of its truth, and its certainty must be 
judged as the certainty of a hypothetical judgment. But 

1 See Hegel, Encyclopadie (Anthropologic}, sect. 404. 

39 8 Modality. 

the disjunction according to the ideal prescribed by its 
form is in itself an exposition of the reality that determines 
its parts, and therefore is not a sequence within a presup- 
posed system, but is itself the content of a real system. It 
therefore properly ranks with the generic judgment, to 
which it is affiliated, as quasi-categorical ; and has only the 
imperfection of certainty which arises from the compara- 
tively minute range of reality that is comprehended in any 
such simple system. 

It is obvious from what has been said above that the 
degrees of certainty here discussed are not numerically 
estimable, because they are not reducible to ratios of equal 
alternatives. It may therefore be justifiably complained 
that the phrase ' degree of certainty ' is misplaced, and 
should be transformed into ' stage of logical necessity.' I 
have no objection to some such transformation provided 
that it is distinctly understood that modality affects the 
assertiveness of assertion, that this assertiveness is a matter 
of content and not of the formal copula or reference to self- 
feeling, but that if we extend the notion of the copula to 
include the material or logical grasp by which a complex 
content is fitted on to a complex Reality then we may say 
that Modality is a matter of the Copula. In any case, the 
progressive incorporation of a content with the under- 
standing *, that is, with the organised ideal system by which 
the understanding permanently qualifies the Real, is the 
same thing as the progressive participation of that content 
in the certainty that could only be complete in a judgment 
that should exhaust Reality. 

1 Cp. Whewell's account (see Mill's Logic, i. p. 279) of coming to perceive 
the necessity of a principle which he had before accepted as fact. This is 
merely the acquisition of a precise and coherent insight into its dependence on 
reality. Cp. Book II. chap. vii. 



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M* 1 3 1983